










UNIVERSITY OF ILLINOIS BULLETIN 






ISSUED WEEKLY 






Vol. XVIII JANUARY 24, 1921 No. 21 

(Entered as eecond-class matter Deceember 11, 1912, al the post office at Urbana, Illinois, under the 
Act of August 24, 1912. Acceptance for mailing at the special rate of postage provided for in sec- 
tion 1103, Act of October 3, 1917, authorized July 31, 1918.) 




BUREAU OF EDUCATIONAL RESEARCH— BULLETIN No. 5 




Report of 1 )ivision of 
Educational 1 ests for '19-20 

BY 

WALTER S. MONROE 

Aisistant Director 
Bureau of Educatiotial Research, University of Illinois 

PRICE, 25 CENTS 

PUBLISHED BY THE UNIVERSITY OF ILLINOIS 
URBANA, ILLINOIS 











Moftc 



BUREAU OF EDUCATIONAL RESEARCH-BULLETIN No. 5 



Report of Division of 
Educational Tests for '19-20 



BY. 



WALTER S. MONROE 

Assistant Director 

Bureau of Educational Research 
University of Illinois 




PRICE, 25 CENTS 



PUBLISHED BY THE UNIVERSITY OF ILLINOIS 

URBANA, ILLINOIS 






LIBRARY OF CONGRESS 
pOOVjiiyiENTS DIVISION 



Bulletins of the Bureau of Educational Research 

B. R. Buckingham, Editor 



EDITORIAL INTRODUCTION 

We should like to have the reader consider this monograph as, 
in a certain sense, "chips from the work-shop." We hold that no orga- 
nization, such as that from which this bulletin emanates, should collect 
from users of test materials the results which they have attained in their 
localities and hoard them in miserly fashion for its own purposes. More- 
over, it is not so nominated in the bond. It is understood that when 
copies of score sheets are mailed to us we are to combine them into master 
score sheets and to issue tabulations which will indicate over a wider 
field than any school system affords the conditions disclosed by the tests 
in question. 

Although the Bureau of Educational Research of the University 
of Illinois went out of the business of distributing tests last November, 
there had been collected up to that time a valuable body of data which was 
augmented during the succeeding months until it now appears to justify 
publication. 

Aside, therefore, from chapters three and four, which deal with 
Monroe's Standardized Reasoning Test in Arithmetic and his Timed 
Sentence Spelling Test, the bulletin is devoted to presenting material 
which will make it possible to use a number of tests more intelligently. 
We do not, as Dr. Monroe says, attempt in this bulletin to give directions 
for administering tests or interpreting results. We are mainly concerned 
with what the results are. We are continually receiving questions from 
practical workers in the field. These questions have led us to believe 
that they are much interested in and perplexed by the question of standards. 

Realizing this fact we have tried to make our presentation of re- 
sults as complete and helpful as possible. They are presented substantially 
in three ways. First, we show for each test the median scores by grade. 
In tables devoted to this sort of data we also include the 25- and 75- per- 
centiles. To those who understand the meaning of these latter figures the 
nature of the distribution out of which the medians arise will be made 
evident. If the 75- and 25- percentiles are far apart it means that the 
data are scattering. In other words that the distribution of scores spreads 
over a wide range. 

In order that there might be no doubt about the nature of the 
distribution, we have in the second place presented for each test, the 
number of pupils attaining the indicated scores in each grade to which 



the test was applied. The v^alue of this sort of a showing is greater than 
the practical teacher is likely to realize upon the first inspection. Such a 
table may be converted into a table indicating a distribution in terms of 
percents by dividing each of the entires by the column totals. When the 
table is thus converted it becomes directly comparable with a similar 
table which may be computed for a school or school system. Moreover, 
since it is customary to give the grade medians in connection with this type 
of table — and the custom is followed in this bulletin — the teacher may 
learn from these figures the number and percent of pupils in each grade 
exceeding or falling short of the median of other grades. A teacher may 
likewise discover from such tables a number of subordinate facts concerning 
the test and its applicability to the grades in question — such facts as the 
number of zero scores or scores in the neighborhood of zero, the number of 
perfect or nearly perfect scores, and the nature of the distribution of the 
frequencies throughout. 

But it is probable that the greatest usefulness of these distribution 
tables is of another sort. They are indispensible to those who wish to 
contribute toward the better standardization of tests. For example the 
3000 pupils, more or less, in each grade, whose scores are shown in Table 
II for Monroe's Reasoning Test may reasonably be thought to be insuffi- 
cient for a final standardization. This tabulation provides a form and 
makes a beginning for a more reliable treatment of the test in question. 
Any superintendent can place the pupils whom he has tested — be they few 
or many — in this scheme. Any bureau of research may gather scores 
from schools and school systems in this manner. After a little it may 
(and indeed it should) publish its findings in this manner to the end that 
more reliable standards may be secured. It is because tables of this sort 
are costly to print and of little direct school use that they are so seldom seen. 
They are frequently found after they have been converted into percentage 
distributions, because the latter are useful in making comparisons. But 
they are seldom found in mere frequency form. Yet the presentation of 
such tables is fundamental to cooperative effort. In our judgment every 
research organization ought to publish material in this form. Its high 
value for research purposes should be appreciated in contrast with its 
low value for immediate practical purposes. 

On the other hand, the third form of tabulation is of most value for 
school uses. We are referring to the percentile tables presented in the 
appendix. We are convinced that when this type of material is better 
understood it will be much more widely used. By means of it a teacher 
may "place" a pupil's score among one hundred scores, arranged from 
highest to lowest, these one hundred scores being regarded as typical. 
Thus the percentile table will enable a fifth-grade teacher to state that a 



pupil is (say) twentieth among one hundred typical children of his grade 
in speed of reading, that he is thirty-seventh in the operations of arithmetic, 

fiftieth in spelling, etc. If he is fiftieth in spelling we have the special 
case of the median, which we ordinarily arrive at from another point of 
view. 

In using percentile tables such as those given in the appendix of 
this bulletin, regard must be had for the source of the tables. In its ideal 
form a percentile table is supposed to have been derived from a sufficient 
random sampling of a total "population" — e. g., from the entire fifth-grade 
in American schools, or from the entire number of ten-year-olds in rural 
schools, or from the entire number of graduates of the Chicago high schools. 
In ranking a child's performance one must be sure either that he belongs to 
the population to which the table refers or that the population of both the 
child and the table are indicated. Thus if a fifth-grade pupil obtains a 
score in composition equal to the 80-percentile for his grade, we thereby 
define his rank as twentieth from the top (or eightieth from the bottom) 
among one hundred typical fifth grade children. A pupil thus ranked 
has evidently done rather well compared with pupils of his own grade. 
Very appropriately therefore, we may wish to rank him with reference to 
the sixth grade. His score may perhaps equal the 60-percentile of the 
sixth grade. Accordingly, he would be ranked, on his performance, as 
fortieth from the top among one hundred typical sixth-grade children. 
Similarly he may rank as fiftieth (median) for the seventh grade. 

We submit these percentile tables for their practical utility. They 
are, however, based upon a limited number of cases; and they will be 
somewhat modified when more scores have been made available. 

From the above statements it will be clear that the chief purpose 
of this bulletin is to furnish an accounting of the test results which we have 
received. Nevertheless, we have included two chapters (III and IV) 
on the derivation of Monroe's reasoning tests and timed sentence tests. 
These accounts have been held up a long time. When, therefore, they were 
released, we took account of the demand that has been made for then — 
especially the one relative to the reasoning test — and incorporated them 
into this report of the Division of Educational Tests. 



TABLE OF CONTENTS 

Chapter Page 

I. Introduction 9 

II. Tentative Grade Norms 12 

A. Monroe's Standardized Reasoning Tests in Arithmetic... 12 

B. Buckingham's Scale for Problems in Arithmetic 14 

C. Monroe's Diagnostic Tests in Arithmetic 16 

D. Monroe's Standardized Silent Reading Tests 19 

E. Charters' Diagnostic Language, and Language and Grammar 

Tests 25 

F. Willing 's Scale for Measuring Written Composition 26 

G. Harlan's Test for Information in American History 28 

H. Sackett's Scale in United States History 29 

I. Hotz's First Year Algebra Scale 30 

J. Minnick's Geometry Tests 31 

K. Holley's Sentence Vocabulary Scale 32 

L. Holley's Picture Completion Test for Primary Grades 34 

III. The Derivation of Monroe 's Standardized Reasoning Tests in 

Arithmetic 36 

IV. Monroe's Timed Sentence Spelling Tests AND Pupils' Errors. 48 
Appendix: Percentile Scores 57 

1. Monroe's Standardized Reasoning Tests in Arithmetic. 

2. Monroe 's Standardized Silent Reading Tests. 

3. Charters' Diagnostic Language Tests for Grades III to VIII. 

A. Pronouns 

B. Verbs 

C. Miscellaneous A 

D. Miscellaneous B 

4. Charters' Diagnostic Language and Grammar Tests for 

Grades VII to VIII 

A. Pronouns 

B. Verbs 

C. Miscellaneous 

5. Willing 's Scale for Measuring Written Composition 

6. Harlan 's Test for Information in American History. 

7. Hotz's First Year Algebra Scale 

8. Holley's Sentence Vocabulary Scale. 



CHAPTER I 

INTRODUCTION 

Source of data. In distributing educational tests the Bureau of Edu- 
cational Research has always supplied a duplicate class record sheet on which 
was printed a request that the duplicate be returned after the scores had been 
entered upon it. There has been no effort to follow up the purchasers of the 
tests in order to secure complete returns of the scores. Consequently, this 
report is based upon the scores voluntarily contributed. The bulk of the scores 
are from medium sized cities. Reports have been received from a few large 
cities (population of 100,000 or more) for Monroe 's Standardized Silent Read- 
ing Tests but in no other case has more than one such city reported. Practically 
no scores were reported from rural schools except for Monroe's Standardized 
Silent Reading Tests. Several tests distributed by the Bureau of Educational 
Research are not included in this report for the reason that the number of scores 
reported seemed to be too small to justify any announcement of median 
scores which would be useful as tentative standards. 

Form of the report. The distributions of scores entered upon the class 
record sheets were combined to form a total distribution of scores for each 
yearly grade. No attempt was made to keep separate the scores of the A and 
B sections of the yearly grades. In addition to the median scores for each 
grade the 25- and 75- percentile scores are also given for several of the tests. 
In a few cases the total distributions are given because they have a special 
significance. In the Appendix of this bulletin the 5-, 10-, 20-, 30-, 40-, 50-, 
60-, 70-, 80-, 90-, and 95- percentile scores are given for a number of the tests. 
The publication of the percentile scores is prompted by the desire to make 
possible a more accurate interpretation of a pupil 's score than merely that it is 
above or below the median score. Pupils belonging to any grade exhibit large 
individual differences. For this reason it is frequently desirable to know where 
the score of a pupil places him in the total distribution from which the median 
for his grade was calculated. The percentile scores make it possible to ascer- 
tain for any pupil his approximate position in this total distribution. For 
example, if a pupil 's score is equal or superior to the 80- percentile score for 
his grade, he ranks in the upper 20 percent of all pupils to whom the test was 
given in that grade. 

Time of testing. No attempt was made to organize the giving of the 
tests. Consequently, the scores on which the median and percentile scores are 
based represent testings all the way from September to June. This condition 
makes the derived scores somewhat less useful as tentative grade standards than 
they would be if they were based upon measures obtained at some one fixed 



10 . 

time during the school year. The situation is further complicated by reason 
of the fact that some of the schools reporting have semi-annual promotion while 
others have annual promotion. Some of those which have semi-annual pro- 
motion combined the A and B divisions of each grade in making their reports. 
In order that the median and percentile scores shall have as definite a meaning 
as possible we have estimated for each test the month of the school year which 
the median scores appear to represent. This estimate, however, must be con- 
sidered only approximate. 

An organized, cooperative plan which would have resulted in the tests 
being given on one or more fixed dates during the school year, was not attempted 
for two reasons. In the first place, the complete realization of such a plan was 
impossible because in a large number of school systems the tests were given as 
a part of a local plan. The Bureau of Educational Research believes it is wise 
to encourage this use of educational tests. When the tests are given merely 
as a part of a project originated by a central bureau of research, little use is 
likely to be made of the results by the schools giving them. Their motive is . 
to cooperate with the central bureau, and when this has been completed there 
is a tendency for them to feel that all has been accomplished which may be 
accomplished. This results in a great waste. Information which might be of 
much value to the local school systems is not used. Furthermore, this practise 
tends to engender an attitude toward educational tests that they are merely 
tools of research to be used by central research bureaus and not tools which may 
be used by a school system, or even a teacher, in improving instruction. 

A second reason for not attempting to organize the giving of the tests was 
that tests were distributed in all sections of the United States and in a few 
foreign countries. It would have been impossible to solicit the cooperation of 
all who gave the tests in a plan of organized testing. 

The interpretation of scores by comparison with grade norms. 
It is not the purpose of this bulletin to give detailed suggestions concerning the 
use of the grade medians and percentile scores in the interpretation of the scores 
obtained in any school system by giving the tests. In another place^ the writer 
has indicated in some detail the general procedure to be followed in interpreting 
scores for the purpose of improving instruction. Grade norms are also useful 
in interpreting the scores of pupils for the purpose of classification.- 

In any interpretation of scores, either individual or group, it is necessary 
to bear in mind certain limitations. In the first place none of our educational 
tests yield scores which ar,e absolutely accurate. The errors of measurement 
are large in comparison with the errors made in the measurement of physical 
objects. Errors larger than the difference between the median scores for suc- 



^Monroe, Walter S. "Improvement of Instruction Through the use of Educational 
Tests," Journal of Educational Research, I (February, 1920), 96-102. 

^Buckingham, B.R. "Suggestions for procedure following a testing program^I, 
Reclassification," Journal of Educational Research, II (December, 1920), 787-801. 



11 

•cessive school grades frequently occur although in the case of our better tests 
the majority of the errors are less. These errors of measurement are chance 
errors and for that reason tend to neutralize each other in the median and average 
scores of groups. Therefore, the group scores are more accurate than individual 
scores. However, in interpreting either type of scores one should bear in mind 
the possible errors of measurement which they may include. 

In the second place the score which a pupil makes on any subject- 
matter test, such as reading, arithmetic, history, or language, depends in part 
upon his general intelligence. Pupils belonging to any school grade differ widely 
with respect to their general intelligence and consequently may be expected to 
differ in their achievements. For this reason some pupils belonging to a given 
grade should have scores above the median, while others may be expected to 
have scores below the median because of their differences in capacity to learn. 
There are also differences in the average general intelligence of pupils belonging 
to the same school grade. For example, the average general intelligence of the 
fifth-grade pupils in one school may be a year or more above that of the fifth- 
grade pupils in another school. It is unfair to both pupils and teachers to 
interpret achievement scores without recognizing the differences which may exist 
in the general intelligence of the pupils. To do so will frequently result in 
arriving at erroneous conclusions. Hence, grade standards such as are given 
in this report must be used with due caution. 

Chapters III and IV contain reports of studies which were made by the 
writer during the time he was Director of the Bureau of Educational Measure- 
ments and Standards of the Kansas State Normal School, Emporia, Kansas. 
These reports were originally prepared for publication by that institution. 
Permission has been obtained to incorporate them in this bulletin. In doing 
this the manuscript has been only slightly revised. Chapter III gives an ac- 
count of the derivation of the Monroe Standardized Reasoning Tests in Arith- 
metic. Chapter IV contains a description of the derivation of Monroe 's Timed 
•Sentence Spelling Tests and a report of a study of pupils* errors in spelling 
based upon them. 



CHAPTER II 



TENTATIVE GRADE NORMS 



The percentile scores as well as the median scores which are given in 
this chapter should be used only as tentative grade standards. For several 
of the tests the number of scores on which these are based is so small that the 
standards can not be thought of as final. When other scores are added to the 
distributions, it is likely that different medians will be obtained. Furthermore, 
such standards should always be thought of as representing the average of 
present conditions and not as being ideal standards or what ought to be. 

A. Monroe's Standardized Reasoning Tests in Arithmetic 

The derivation of these tests, which consist of a series of one- and two- 
step problems, is described in Chapter III. For each problem two values were 
calculated, "correct principle value," or P, and "correct answer value," or C. 
These values represent the credit which is to be given for solving the problem 
correctly in principle and for obtaining the correct answer. Each problem 
is marked for correct principle. If a problem is solved correctly in principle 
it is further marked with reference to correct answer. A pupil does not receive 
credit for a correct answer if the problem was solved by the wrong principle. 
The directions for administering the tests provide for having the pupils mark 
the problem on which they are working at the end often minutes. In this way 

TABLE I. MONROE'S STANDARDIZED REASONING TESTS IN ARITHMETIC. 
FORM I. GRADE NORMS FOR APRIL TESTING 





Grade 




IV 


V 


VI 


VII 


VIII 


Correct Principle 












Number of pupils. 


2932 


3027 


3498 


2796 


2472 


25-percentiIe 


6.2 


12.1 


10.0 


13.8 


11.5 


Median 


11.3 


19.2 


14.2 


19.7 


17.2 


75-percentile 


16.8 


25.9 


19.4 


24.7 


22.8 


*Rate 












Number of pupils 


1412 


1705 


1699 


1717 


1642 


25-percentile 


5.2 


8.0 


6.4 


8.0 


5.3 


Median 


7.8 


11.2 


8.7 


11.2 


7.5 


75-percentile 


8.1 


15.1 


12.1 


14.5 


10.9 


Correct Answers 












Number of pupils 


2968 


2996 


3518 


2803 


2515 


25-percentile 


4.1 


7.1 


6.9 


9.4 


5.1 


Median 


7.0 


11.3 


10.4 


13.4 


9.0 


75-percentile 


10.7 


15.5 


14.0 


17.4 


13.0 



"Sum of correct principle values of problems done correctly within ten minutes. 



13 

a rate score may be obtained. It is the sum of the "principle vakies" of the 
problems which are solved correctly in principle within ten minutes. However, 
the obtaining of the rate score is optional, and it was reported in only about 
half of the cases. 

There are two forms of these tests. These forms were constructed so 
that they were expected to be equivalent. Experience in using them suggests 
that they are not equivalent, although data are lacking at this time on which 
a statement concerning their comparability may be based. No scores are 
reported for Form 2 because the returns received for this form included an 
insufficient number of cases. 

Test I is given in Grades IV and V, Test II in Grades VI and VII, and 
Test III in Grade VIII. The tests were not constructed so that the scores 
yielded by the different tests are comparable. Therefore, direct comparisons 
can not be made between the fourth and fifth grade scores and between the 
seventh and eighth grade scores. 

TABLE II. MONROE'S STANDARDIZED 
REASONING TESTS IN ARITHMETIC 
FORM I, CORRECT PRINCIPLE 



Score* 


Grade 














IV 


V 


VI 


VII 


VIII 


43 


3 


11 








41 




5 








39 


7 


20 








37 


1 


21 








35 


12 


89 








33 


11 


56 








31 


26 


137 






56 


29 


25 


120 


47 


127 


94 


27 


40 


191 


93 


262 


63 


25 


80 


191 


131 


202 


171 


23 


89 


223 


135 


242 


214 


21 


124 


269 


248 


304 


233 


19 


130 


207 


280 


322 


214 


17 


161 


211 


306 


259 


217 


15 


248 


231 


328 


225 


237 


13 


260 


219 


470 


225 


203 


11 


298 


167 


425 


193 


201 


9 


267 


166 


374 


134 


133 


7 


294 


148 


276 


103 


154 


5 


304 


140 


191 


52 


121 


3 


230 


94 


123 


30 


87 


1 


185 


54 


49 


18 


51 





137 


57 


22 


8 


23 


Total 


2932 


3027 


3498 


2706 


2472 


Median 


11.3 


19.2 


14.2 


19.7 


17.2 



• In this bulletin ail intervals unless other- 
wise noted are expressed in terms of their 
lower limits. 



14 

Table I gives the grade medians, 25-percentile, and 75-percentile scores^ 
for correct principle, correct answer, and rate. The distributions of scores for 
correct principle are given in Table II. These indicate that Test I is too 
difficult for a number of pupils in the fourth and fifth grades. In the construc- 
tion of the tests no effort was made to include very easy problems. In fact,^. 
as is shown in Chapter III, the difficulty of a problem was not considered as 
a basis for selection. In none of the other grades do the zero scores amount to 
as much as one per cent of the total. In the seventh grade nearly five percent 
of the pupils made perfect scores. 

References 

Willing, M. H. "The Encouragement of Individual Instruction by Means of Standard- 
ized Tests," Journal of Educational Research, I (March, 1920), 193-198. 

Results from the Monroe Scandardized Reasoning Tests are used to illustrate how such: 
work as the title mentions may be carried on. Suggestions for diagnosis of faults, remedial 
measures, etc. are given. 

B. Buckingham's Scale for Problems in Arithmetic. 

The problems for Buckingham 's scale were selected largely on the basis 
of diffculty. Division One is for Grades III and IV, Division Two for Grades 
V and VI, and Division Three for Grades VII and VIII. The problems of 
Division One increase by steps of approximately 0.3 P. E. from 2.7 to 5.3. 
The problems of Division Two increase by similar steps of difficulty from 5.5 
to 7.3, and the problems of Division Three increase from 7.5 to 9.4. In scoring 
the test papers attention is given only to the numerical accuracy of the answers.. 
A pupil's score is the difficulty value of the hardest problem which he answers 
correctly, unless he has failed on one or more previous problems. In that case, 
a correction is made by subtracting from the value of the hardest correctly 
solved problem 0.3 for each failure in Division One, or 0.2 for each failure in 
Division Two or Three. Thus, if a pupil solved the first six problems in Divi- 
sion One, his score is 4.2; but if he fails on the 4th and 5 th (otherwise succeeding, 
through the 6th), his score is 3.6— i.e., 4.2 — 2 x 0.3. 



TABLE III. BUCKINGHAM 'S SCALE FOR PROBLEMS IN ARITHMETIC. 
I. GRADE NORMS FOR JUNE TESTING. 



FORM 





Grade 




III 


IV 


V 


VI 


VII 


VIII 


No. of pupils 
25-Percentile 
Median 
75-Percentile 


4181 
3.4 
3.8 
4.3 


4589' 
4.2 
4.6 

5.2 


7142 
5.7 
5.9 
6.3 


5927 
5.9 
6.4 
6.8 


6632 
7.6 
7.8 
8.3 


5269 
7.7 
8.2 
8.7 



Although the three divisions of the scale were constructed so that it was 
expected that the scores obtained from the different divisions would be com- 



15 

parable, the grade medians given in Table III clearly indicate that the scores 
are not comparable. The increase in the median scores from the third grade 
to the fourth grade is 0.8. The increase from the fourth grade to the fifth grade 
is 1.3. A similar variation is found in the differences between the subsequent 
grades. Therefore, the scores obtained by the different divisions of the scale 
are not comparable. The reason for this is that the pupils taking Division Two 
or Division Three do not have an opportunity to do the problems of the lower 
divisions. If they did, a number of them would fail to do all of them correctly. 
Thus, they would receive a score lower than that which they receive when 
taking only the higher divisions. 

TABLE IV. BUCKINGHAM'S SCALE FOR 

PROBLEMS IN ARITHMETIC. FORM I 

GRADE DISTRIBUTIONS FOR 

JUNE TESTING 









Grade 






















III 


IV 


V 


VI 


VII 


VIII 


9.0 










328 


699 


8.5 








6 


782 


1084 


8.0 




1 


4 


11 


1349 


1290 


7.5 






14 


13 


2931 


1740 


7.0 






240 


775 


58 


44 


6.5 




2 


1012 


1886 






6.0 




6 


1540 


1504 






5.5 





21 


3663 


1569 






5.0 


131 


1069 


106 


57 






4.5 


490 


1474 


14 


12 






4.0 


815 


^ 863 










3.5 


1305 


798 










3.0 


967 


255 










2.5 


298 


75 













173 


25 


549 


94 


1184 


412 


Total 


4181 


4589 


7142 


5927 


6632 


5269 


Median 


3.8 


4.6 


5.9 


6.4 


7.8 


8.2 



In Table IV the total distributions are given. Evidently a division of 
the scale higher or lower than that designed for the grade has been used in a 
few cases. The distributions are significant in that they show that the divi- 
sions of the scale are too difficult for the respective grades. The percent of 
pupils making zero scores in the third, fifth, seventh, and eighth grades is so 
large that the scale as now published must be considered unsatisfactory for 
these grades. This condition could be remedied in the case of Division Two 
and Division Three by giving the next lower division to the pupils who make 
zero scores. In the case of Division One, the scale will have to be extended 
downward by adding less difficult problems. 



16 



References 

First Annual Report, Bureau of Educational Research, University of Illinois, pp. 21-22. 
These pages contain a very brief suggestion of what was done along the line of this scale 
that seemed to justify its construction, also a short description of the scale. 

Buckingham, B.R. "Notes on the Derivation of Scales in School Subjects, with Special 
Application to Arithmetic," Fifteenth Yearbook of National Society for the Study of 
Education, Part I, pp. 23-40. 

This presents a report of a series of problems which was given to a number of school children 
in New York and other cities. The results are given and discussed, especially with reference 
to locating the problems on a scale. Although this scale is not the one now in use, it is 
similar to it. 

C. Monroe's Diagnostic Tests in Arithmetic. 

Monroe's Diagnostic Tests in Arithmetic consist of four parts. Part I 
includes Tests 1 to 6. Part II includes Tests 7 to 11. These tests involve only- 
integers. Part III includes Tests 12 to 16, which consist of examples involving 
common fractions. Part IV includes Tests 17 to 21, which consist of examples 
involving multiplication and division of decimal fractions. Tables V and VI 



TABLE V. MONROE'S DIAGNOSTIC TESTS IN ARITHMETIC. 
MEDIANS FOR APRIL TESTING. RATE (NUMBER 
OF EXAMPLES ATTEMPTED) 



GRADE 





Grade 




IV 


V 


VI 


VII 


VIII 


Part I 












(Approximate number of pupils) 


900 


480 


590 


600 


600 


Test 1 


7.2 


11.6 


13.3 


12.6 


14.0 


Test 2 


4.1 


7.2 


9.3 


8.6 


9.2 


Test 3 


3.3 


5.0 


5.8 


5.7 


7.2 


Test 4 


2.0 


3.2 


4.0 


4.7 


5.7 


Tests 


3.9 


4.8 


5.6 


5.7 


6.2 


Test 6 


1.7 


2.7 


3.1 


3.0 


4.0 


Part II 












(Approximate number of pupils) 


380 


760 


610 


520 


460 


Test? 


3.8 


4.2 


5.5 


5.3 


6.3 


Tests 


3.0 


4.1 


5.5 


6.1 


6.6 


Test 9 


4.8 


5.9 


8.2 


8.6 


9.8 


Test 10 


2.8 


3.2 


5.3 


5.3 


6.7 


Test 11 


1.6 


2.2 


2.2 


2.9 


3.7 


Part III 












(Approximate number of pupils) 




370 


1000 


580 


560 


Test 12 




5.8 


7.6 


8.6 


9.4 


Test 13 




4.5 


5.4 


6.0 


6.0 


Test 14 




5.2 


7.1 


8.1 


8.7 


Test 15 




6.2 


7.1 


7.7 


8.1 


Test 16 




5.7 


7.4 


8.0 


9.1 


Part IV 












(Approximate number of pupils) 






440 


900 


660 


Test 17 






3.6 


3.5 


4.5 


Test 18 






11.9 


11.5 


12.9 


Test 19 






5.8 


4.5 


5.3 


Test 20 






12.5 


11.1 


13.5 


Test 21 






5.1 


4.3 


4.8 



17 

give the median scores for these tests in terms of rate (number of examples 
attempted) and accuracy (percent of examples done correctly). In order to 
simplify the administration of these tests the plan of scoring has been changed 
so that the pupil is now given only one score, the number of examples right. 
In Table VII tentative grade norms are given in terms of this score. 

In the interest of economy, both of cost of the tests and time required 
for their administration, most of the tests of this series were made so short that 
there is a lack of discrimination between pupils. For example, the increase 
in the number of examples attempted from grade to grade is frequently less than 
one example. The shortness of the tests also makes the errors of measurement 
relatively large. 

This group of tests was designed for diagnostic purposes, i. e., it was in- 
tended to measure separately the abilities of pupils to do the important types of 



TABLE VI. MONROE 'S DIAGNOSTIC TESTS IN ARITHMETIC. GRADE 

MEDIANS FOR APRIL TESTING. ACCURACY (PERCENT 

OF EXAMPLES CORRECT) 





Grade 




IV 


V 


VI 


VII 


VIII 


Part I 












Approximate number of pupils 


900 


480 


590 


600 


600 


Test 1 


100 


100 


100 


100 


100 


Test 2 


66.6 


86.8 


100 


100 


100 


Test 3 


56.5 


72.3 


80.8 


82.0 


87.6 


Test 4 


28.0 


55.1 


71.9 


79.8 


85.4 


Tests 


52.5 


61.7 


66.9 


67.9 


75.1 


Test 6 


22.4 


49.5 


64.0 


77.5 


100 


Part 11 












Approximate number of pupils 


380 


760 


610 


520 


460 


Test? 


63.2 


65.1 


75.9 


76.3 


81.6 


Tests 


30.4 


52.9 


66.9 


79.8 


78.5 


Test 9 


75.0 


86.3 


91.2 


93.1 


100 


Test 10 


35.2 


58.4 


72.1 


72.3 


81.9 


Test 11 


22.4 


35.5 


53.4 


65.0 


68.2 


Part III 












Approximate number of pupils 




370 


1000 


580 


560 


Test 12 




35.5 


32.0 


33.6 


49.0 


Test 13 




38.0 


29.2 


36.0 


53.9 


Test 14 




57.5 


70.3 


79.6 


86.0 


Test 15 




37.5 


30.0 


33.6 


45.5 


Test 16 




38.5 


36.8 


59.1 


70.2 


Part IV 












Approximate number of pupils 






440 


900 


660 


Test 17 






37.6 


36.4 


53.2 


Test 18 - 






100 


100 


100 


Test 19 






39.6 


47.0 


61.7 


Test 20 






100 


100 


100 


Test 21 






35.6 


44.0 


51.3 



18 

examples in the field of the operations of arithmetic. A weighted sum of a 
pupil 's scores on such a group of tests would yield a general measure of his 
ability in this field.' 

TABLE VII. MONROE'S DIAGNOSTIC TESTS IN ARITHMETIC. GRADE 
MEDIANS FOR APRIL TESTING. NUMBER OF EXAMPLES CORRECT 



•>. 


Grade 




IV 


V 


VI 


VII 


VIII 


Part I 












Approximate number of pupils 


900 


480 


590 


600 


600 


Test 1 


7.2 


11.6 


13.3 


12.6 


14.0 


Test 2 


2.8 


6.2 


9.3 


8.6 


9.2 


Test 3 


1.9 


3.6 


4.7 


4.7 


6.4 


Test 4 


.6 


1.7 


2.9 


3.6 


4.8 


Test 5 


2.0 


3.0 


3.7 


3.8 


4.4 


Test 6 


.4 


1.3 


2.0 


2.3 


4.0 


Part II 












Approximate number of pupils 


380 


760 


610 


520 


460 


Test 7 


2.4 


2.7 


4.2 


4.0 


5.1 


Tests 


.9 


2.2 


3.7 


4.8 


5.2 


Test 9 


3.6 


5.1 


7.5 


8.0 


9.8 


Test 10 


1.0 


1.8 


3.8 


3.8 


5.5 


Test 1 1 


.4 


.8 


1.2 


1.8 


2.4 


Part III 












Approximate number of pupils 




370 


1000 


580 


560 


Test 12 




2.0 


2.4 


2.9 


4.6 


Test 13 




1.7 


1.6 


2.2 


3.2 


Test 14 




3.0 


5,0 


6.5 


7.4 


Test 15 




2.3 


2.1 


2.6 


3.7 


Test 16 




2.2 


2.7 


4.7 


6.4 


Part IV 












Approximate number of pupils 






440 


900 


660 


Test 17 






1.4 


1.3 


2.4 


Test 18 






11.9 


11.5 


12.9 


Test 19 






2.4 


2.1 


3.3 


Test 20 






12.5 


11.1 


13.5 


Test 21 






1.8 


1.9 


2.5 



References 

Finley, G. W., A Comparative Study of Three Diagnostic Arithmetic Tests. Colorado 
State Teachers College Bulletin, Series XX, No. 4. 

This reports a study made of the Cleveland Survey Tests, The Woody Arithmetic Scales and 
Monroe's Diagnostic Tests in Arithmetic. The tests were given on six successive days to 
some 60 eighth grade pupils. The scores made are given in detail, compared with each other 
and with scores obtained elsewhere. 

Monroe, W. S., "A Series of Diagnostic Tests in Arithmetic," Elementary School 
Journal, XIX, (April, 1919), 585-607. 

This article discusses the types of examples in the four fundamental operations, the question 
of "one dimensional" vs. "two dimensional" tests, and thus establishes the theoretical bases 
of the tests presented. The series is described, a distribution of scores made thereon is ana- 
lyzed, and the value of using such tests pointed out. 

'See the group of tests on the operations of arithmetic included in the Illinois Examination. 



19 

Uhl, W. L., "The Use of Standardized Materials in Arithmetic for Diagnosing Pupils' 
Methods of Work," Elementary School Journal, XVIII, (November, 1917), 215-218. 
This article contains no reference to the Monroe Tests, but describes an experiment in diag- 
nosis similar to that made possible by their use. Both finding specific faults and remedying 
them is considered briefly. 

D. Monroe's Standardized Silent Reading Tests. 

Monroe's Standardized Silent Reading Tests have been used so widely 
that a detailed description here is unnecessary. Each test consists of several 
exercises, each of which has been assigned a rate value and a comprehension 
value. The rate value is based upon the number of words in the exercise and 
the comprehension value is based upon the rate and accuracy with which pupils 
were found to be able to do the exercise. Test I is for Grades III, IV, and V, 
Test II is for Grades VI, VII, and VIII, and Test III is for the high school. 
There are three forms of Tests I and II. There are only two forms of Test III, 

The different forms of these tests were constructed so that they were 
expected to be equivalent. The use of the forms, however, indicates that they 
are not equivalent. In order to study the degree of equivalence of the three 
forms, copies of the different forms were arranged in alternate order before the 
test papers were distributed to the pupils. This plan results in the first, 
fourth, seventh, tenth, etc. pupil having a copy of Form 1. The second, 
fifth, eighth, eleventh, etc. pupil would have a copy of Form 2. The third, 
sixth, ninth, twelfth, etc. pupil would have a copy of Form 3. By this plan 
each form of the test is given to similar samples of the school population. 

Test I was given to approximately 775 pupils and Test II was given to 
approximately 645. The numbers of pupils taking the different forms in each 
grade differed slightly. This is an accidental result of the way in which the 
test papers were arranged. The average and the standard deviation have been 
calculated for each distribution of scores. In general the pupils made higher 
scores on Forms 2 and 3 than they did on Form 1. The standard deviations 
are also unequal. This suggests that the exercises of the different forms of 
the tests make somewhat irregular scales. 

The formula for reducing the scores obtained from one scale to equivalent 
scores on another scale is as follows: 



S,=-^S,+ 



(^y,- p-Av^l 



In this formula Sj is the equivalent score in Form 1 and S2 the obtained sorec in 
Form 2. Avi refers to the average of the scores obtained from Form 1, Av2 
refers to the average of the scores obtained from Form 2. o-i is the standard 
deviation of the distribution of the Form 1 scores and <^2 is the standard devia- 
tion of the distribution of the Form 2 scores. This formula is based upon the 
usual assumption that the deviations from the average are equal when expressed 
in terms of the standard deviation of the distribution; in other words that 



20 



Si - Avi 



AV2 



<^!! 



When this equation is solved for Si we obtain the formula as given above. 
Since the scores on Form 1 are in general smaller than the scores on the other 
two forms it was decided to reduce both the Form 2 and the Form 3 scores to 
the equivalence of Form 1 scores. The application of the above formula 

involves the determination of the numerical value of the ratio of -^ by which 

the Form 2 score is to be multiplied and the determination of the numerical 
equivalent of the constant terms of the formula, (i.e., of the expression in 
parentheses). This latter numerical equivalent may be plus or minus. When 
it is positive it is to be added and when negative it is to be subtracted. 



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In Table VIII, the number of pupils, the average score and the standard 
deviation is given for each form of each test. In the last two columns the 
multiplier and the constant term in the above formula are given for Form 2 
and Form 3. These can be used in reducing scores obtained from Form 2 or 
Form 3 to the basis of Form 1. In securing data for these determinations, each 
test was given in each of the three grades for which it is intended. Except 
in the eighth grade the number of pupils in the different grades was approxi- 
mately the same. The correction numbers were calculated for each grade 
separately. Since they were found to be approximately the same it was decided 
to combine the scores from the different grades and compute a single set of 
correction numbers for each test. 

The grade medians calculated from the distributions of the scores yielded 
by the different forms furnished additional information concerning the degree 
of their equivalence. This information is not in complete agreement with that 
obtained by the study described. Although it is less accurate it deserves some 
consideration in the formulation of a set of rules for translating the scores 
obtained from one form to the basis of another form. In Table IX-A grade 
medians for all forms are given, and in Table IX-B correction numbers which 
may be used in reducing scores from Form 2 or Form 3 to Form 1. The cor- 
rection numbers are based primarily on the results of the study just described 
but some weight was given to the information furnished by the tabulations of 



TABLE IX-A. MONROE 'S STANDARDIZED SILENT READING TESTS. GRADE 
MEDIANS FOR JANUARY AND JUNE TESTING, BASED UPON 130,000 SCORES 





Grade 




III 


IV 


V 


VI 


VII 


VIII 


IX 


X 


XI 


XII 


Form 1 






















Rate 






















January 


52 


70 


87 


90 


100 


106 


83 


85 


90 


96 


June 


60 


79 


94 


96 


104 


108 


86 


87 


94 


100 


Comprehension 






















January 


6.8 


12.7 


17.8 


18.5 


22.8 


26.0 


23.0 


25.4 


27.2 


30.0 


June 


9.3 


15.3 


20.8 


21.0 


24.5 


27.3 


24.0 


26.0 


28.6 


32.0 


Form 2 






















Rate 






















January 


63 


77 


98 


116 


130 


133 


84 


90 


98 


104 


June 


70 


88 


106 


124 


132 


136 


86 


92 


101 


109 


Comprehension 






















January 


8,3 


13.3 


17.2 


18.1 


26.0 


28.2 


25.4 


28.0 


31.0 


33.1 


June 


10.6 


15.6 


20.5 


20.8 


27.3 


29.4 


26.6 


29.4 


32.2 


34.5 


Form 3 






















Rate 






















January 


78 


92 


97 


101 


109 


111 










June 


85 


95 


104 


106 


111 


114 










Comprehension 






















January 


9.3 


14.8 


18.4 


22.2 


26.5 


29.8 










June 


11.9 


16.8 


21.5 


24.4 


28.2 


30.5 











22 



TABLE IX-B. APPROXIMATE CORRECTIONS BY WHICH TO MULTIPLY FORM 2 
AND FORM 3 SCORES TO REDUCE TO THE BASIS OF FORM 1 SCORES 



Rate 


Comprehension 


Test I 


Test II 


Test III 


Test I 


Test II 


Test III 


Form 2 . 88 
Form 3 .78 


.80 
.93 


.94 


.95 
.94 


.93 
.86 


.90 



the scores obtained from the different forms. This is the explanation of some 
apparent inconsistencies in the reductions to the basis of Form 1 . 

It should be noted that the scores of the different tests in this series are 
not comparable. This is to be expected in the case of the rate scores but in 
the case of the comprehension scores an effort was made to have the different 
tests yield comparable scores. This attempt was not successful. 

The grade distributions which are not published here, show that the tests 
are too short for the time allowed. In order to secure accurate measures of 
the abilities of the best readers it will be necessary either to lengthen the test 
or to shorten the time allowed. The wide spread use of these tests has revealed 
other defects. Instead of attempting to remedy these defects in the present 
series it was decided to derive an entirely new series. These have been issued 
under the tide of " Monroe 's Standardized Silent Reading Tests, Revised." 
Three forms of Tests I and II are now available. They were originally pub- 
lished as a part of the Illinois Examination but are now printed separately. 

In Tables X-A and X-B we have assembled a miscellaneous collection 
of grade medians. These are published because a number of requests have 
been received for just this type of information. 



References 

Monroe, W, S., "Monroe's Standardized Silent Reading Tests," Journal of Edu- 
cational Psychology, IX, (June, 1918), 303-312. 

The deriviation of the tests more or less based upon the Kansas Silent Reading Test plan, 
is briefly sketched. The investigation of weighting and timing is outlined, a sample of the 
tests is given and some few data concerning results from pupils. 

Barnes, Harold, "Reorganization of Classes Based on the Monroe Silent Reading 
Tests," University oj Pennsylvania Bulletin, vol. XX, No. 1, 119-123. 

This article recounts the use made of these tests in the elementary grades of Girard College. 
Not only are the scores presented, but also the resulting organization upon the basis of ability 
as shown on the tests is described. 

Kelly, F. J., "Kansas Silent Reading Tests," Journal of Educational Psychology, 
VII, (February, 1916), 63-80. 

The author of these tests, which were the forerunners of Monroe 's Standardized Silent Reading 
Tests, gives a brief statement of the construction, administration, and use of the tests, follow- 
ing it with a more detailed statement of results secured in nineteen Kansas cities. 

Lloyd, S. M. and Gray, C. T., "Reading in a Texas City, Diagnosis and Remedy," 

University of Texas Bulletin, No. 1853. 



23 

This bulletin gives an account of a study of the reading situation in Austin. The Monroe 
tests were given in grades 3-7. Results obtained are analyzed at considerable length, 
measures to improve the situation are discussed, and improvement after a period of special 
emphasis on reading is shown. 

Pressey, S. L. and L. W., "The Relative Value of Rate and Comprehension Scores 
in Monroe's Silent Reading Test, as Measures of Reading Ability," School and Society, 
Gune 19, 1920), 747-49. 

In a brief discussion of the above subject, the writers present results of correlating teachers* 
estimates of reading ability with rate and comprehension scores, also the latter with each 
other. They conclude that comprehension scores may tell us all the tests can about children's 
ability in reading. 



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25 

E. Charters Diagnostic Language Tests, and Diagnostic 
Language and Grammar Tests. 

There are two groups of these tests: (1) The Diagnostic Language 
Tests, designed for Grades III to VIII inclusive, which inckide. Pronouns, 
Verbs, (formerly Verbs A), Miscellaneous A (formerly Miscellaneous), Mis- 
cellaneous B (formerly Verbs B); (2) The Language and Grammar Tests, 
designed for Grades VII and VIII, which include Pronouns, Verbs (formerly 
Verbs A) and Miscellaneous A (formerly Miscellaneous). The Language 
Tests consist of a number of sentences most of which are grammatically in- 
correct. If a sentence is correct the pupil makes a cross on the dotted line 
below the sentence. If the sentence is not right the pupil is required to put 
the correct words on the dotted line below it. In the Language and Grammar 
Tests the pupil is required in addition to write the rule on which the correction 
is based. The pupil 's score is the number of exercises which he does correctly. 
Since the sentences which make up the tests were selected as representative 
of the errors which pupils make, a pupil 's performance on the tests gives a 
diagnosis of his abilities in the field of these tests. 

There are two forms of these tests. The second form, however, was not 
published until September, 1920. Consequently, the scores reported in this 
bulletin are based on Form 1. Although the two forms were constructed so that 
Form 2 might be expected to be equivalent to Form 1, there is available at 
this time no information concerning the degree of their equivalence. 



TABLE XI A. GRADE NORMS FOR CHARTERS' DIAGNOSTIC LANGUAGE 
TESTS. MARCH TESTING 





Grades 




III 


IV 


V 


VI 


VII 


VIII 


*MlSCELLANEOUS A 














Number of Pupils 


386 


669 


668 


845 


758 


494 


25-percentile 


4.0 


5.8 


8.1 


11.8 


14.0 


16.6 


Median 


6.7 


9.3 


11.6 


16.5 


18.9 


22.3 


75-percentile 


13.3 


13.6 


16.0 


21.7 


24.4 


27.1 


tMlSCELLANEOUS B 














Number of Pupils 


230 


430 


307 


475 


412 


294 


25-percentile 


3.0 


10.6 


15.7 


19.8 


23.5 


28.7 


Median 


7.9 


17.8 


22.0 


27.3 


29.4 


32.0 


75-percentiIe 


14.8 


24.5 


27.6 


32.4 


33.7 


36.8 


**Verbs 














Number of pupils 


365 


403 


373 


478 


539 


638 


25-percentile 


7.3 


12.9 


17.2 


19.0 


•22.7 


28.6 


Median 


12.6 


17.7 


22.6 


24.3 


27.7 


32.8 


75-percentile 


18.8 


22.7 


28.4 


29.3 


31.9 


36.1 


Pronouns 














Number of pupils 


787 


864 


895 


1344 


1566 


1253 


25-percentile 


8.9 


11.1 


14.2 


17.0 


19.6 


23.1 


Median 


13.6 


15.1 


18.5 


21.4 


24.5 


29.0 


75-percentile 


19.8 


20.3 


22.6 


25.7 


29.5 


34.0 



* Formerly Miscellaneous 
t Formerly Verbs B 
** Formerly Verbs A 



26 



TABLE XI-B. GRADE NORMS FOR 

CHARTERS' DIAGNOSTIC LANG- 

GUAGE AND GRAMMAR TESTS 

MARCH TESTING 





Grades 




VII 


VIII 


Miscellaneous 






Number of pupils 


332 


362 


25-percentile 


2.9 


6.1 


Median 


6.3 


11.9 


75-percentile 


11.7 


18.7 


Verbs 






Number of pupils 


434 


497 


25-percentile 


2.8 


6.9 


Median 


7.8 


14.0 


75-percentile 


22.9 


24.1 


Pronouns 






Number of pupils 


332 


362 


25-percentile 


4.4 


8.5 


Median 


8.0 


17.1 


75-percentile 


16.7 


26.0 



References 

Charters, W. W., "Minimum Essentials in Elementary Language and Grammar," 
Sixteenth Yearbook of the National Society for the Study oj Education. Part I, 85-110. 
This article gives a brief account of a number of studies of language and grammar errors made 
by school children, with tables of results. These studies were the basis of the content of 
Charters' tests. 

Sixth Conference on Educational Measurements. Bulletin of the Extension Division, 
Indiana University, Vol. V, No. I, pp. 6-12 and 13-24. 

These two discussions by Charters give a rather general discussion leading up to a brief 
account of the development and form of the tests, followed by some suggestions as to their use. 

Charters, W. W., "Constructing a Language and Grammar Scale," Journal of 
Educational Research, I (April, 1920), 249-257. 

The tests herein considered are a revision of those referred to above. The writer gives a 
short description of their derivation, use, scoring, etc. The question of weighting is discussed 
and the reason for its elimination given. 



F. Willing 's Scale for Measuring Written Composition 

The Willing Scale for Measuring Written Composition differs from other 
composition scales in that an attempt is made to secure separate measures of 
"form value" and "story value." The "form value" of a pupil's composition 
is based upon his errors in grammar, punctuation, capitalization, and spelling. 
In order to make the scores in form value comparable, the number of errors 
which the pupil makes is multiplied by 100 and divided by the number of words 
in his composition. The quotient is the number of errors per hundred words. 
The "story value" of a pupil's composition is its value when errors of grammar 
punctuation, capitalization, and spelling are neglected. This value is measured 
by means of the scale. 



27 

TABLE XII. GRADE NORMS FOR WILLING 'S SCALE FOR MEASURING 
WRITTEN COMPOSITION, MARCH TESTING 





Grade 




III 


IV 


V 


VI 


VII 


VIII 


Approx. No. of Pupils 


325 


580 


705 


695 


570 


130 


Story Value 














25-percentile 


30.5 


43.4 


55.7 


60.9 


65.9 


65.3 


Median 


41.5 


58.7 


68.1 


74.0 


76.6 


79.0 


75-percentile 


54.8 


74.5 


78.8 


85.2 


86.6 


86.2 


Form Value (Errors per 100 Words) 














25-percentile 


11.7 


6.2 


3.6 


3.2 


2.6 


2.3 


Median 


18.5 


10.7 


6.8 


5.8 


4.4 


4.4 


75-percentile 


26.0 


17.3 


10.9 


9.8 


6.4 


7.0 



The grade distributions given in Tables XIII and XIV indicate that 
the scale needs to be extended at both ends. It does not contain steps low 
enough in story value to provide adequate measures for many compositions 
contributed by pupils in the third and fourth grades. Neither does it provide 
adequate measures for the best compositions in grades beyond the fourth. 
For practical purposes these limitations are not serious because when a pupil's 
composition is as poor as 20 on this scale the pupil needs special attention. 
When a pupil writes a composition as good as 90 on this scale it is likely that 
special instruction is superfluous. In addition it may be pointed out that the 
median score of a class is probably not affected by these limitations of the scale. 



TABLE XIII. WILLING 'S SCALE FOR MEASUR- 
ING WRITTEN COMPOSITION. GRADE DISTRI- 
BUTIONS FOR MARCH TESTING 









Grade 






Story Value 












Score* 


IV 


V 


VI 


VII 


VIII 


IX 


90 


7 


28 


52 


81 


95 


14 


80 


6 


67 


105 


177 


141 


48 


70 


8 


91 


168 


147 


150 


25 


60 


28 


91 


146 


123 


107 


21 


50 


60 


98 


110 


75 


41 


12 


40 


60 


90 


77 


49 


31 


4 


30 


75 


66 


39 


32 


5 


4 


20 


76 


48 


8 


8 


o 


1 


Total 


320 


579 


705 


692 


572 


129 


Median 


41.5 


58.7 


68.1 


74.0 


76.6 


79.0 



*These intervals are expressed in terms of their mid- 
points. 

References 

Willing, M. H., "The Measurement of Written Composition in Grades IV to VIII 
English Journal, VII (March, 1915), 193-202. 



28 • 

The writer explains and outlines the measurement of written composition especially in con- 
nection with the Denver and Grand Rapids surveys. The method of constructing the scale, 
its use, scoring, results obtained, etc. are discussed, and the scale reproduced. 

The Denver Survey, 1916, Part II, pp. 59-63, and the Grand Rapids Survey, 1916, pp. 
85-105, give accounts of the use of this scale. The latter contains rather complete tables and 
graphs of pupil achievement, and comparisons of results with those obtained in Denver 



TABLE XIV. WILLING 'S SCALE FOR MEASURING 
WRITTEN COMPOSITION. GRADE DISTRI- 
BUTIONS FOR MARCH TESTING 









G 


RADE 






















IV 


V 


VI 


VII 


VIII 


IX 


30 


50 


14 


3 


5 


2 




27 


24 


17 


1 ' 


4 


3 




24 


22 


27 


8 


4 


1 




21 


32 


29 


9 


4 


1 




18 


43 


38 


19 


18 


4 




15 


29 


51 


45 


17 


15 


2 


12 


42 


56 


52 


48 


28 


4 


9 


34 


120 


105 


96 


49 


12 


6 


32 


79 


149 


140 


131 


21 


3 


14 


98 


170 


199 


200 


49 





5 


41 


141 


158 


138 


41 


Total 


327 


570 


702 


693 


573 


129 


Median 


18.5 


10.7 


6.8 


5.8 


4.5 


4.4 



* Errors per 100 words. 

G. Harlan's Test for Information in American History 

This test consists of ten exercises in the field of American History and 
is designed for use in the seventh and eighth grades. Each exercise consists 
of two or more parts. The maximum score which a pupil may receive is 100. 



TABLE XV. GRADE NORMS FOR 

HARLAN'S TEST OF INFORMATION 

IN AMERICAN HISTORY. MAY 

TESTING 





Grade 




VII 


VIII 


Number of pupils 
25-percentile 
Median 
75-percentile 


1109 
30.1 
43.9 

57.3 


1691 
45.7 
68.2 
83.3 



In Table XVI the distributions of scores for the seventh and eighth 
grades are given. These distributions are of interest because of the very great 



29 



individual differences which they suggest. It is possible that the apparent 
differences are due in a considerable measure to the errors of measurement. 
Since there is only one form of the test no measure of reliability is available. 



TABLE XVI. HARLAN'S TEST OF 
INFORMATION IN AMERICAN 
HISTORY. GARDE DISTRI- 
BUTIONS FOR MAY 
TESTING 



Score 


Grade 


VII 


VIII 


96 
91 
86 
81 
76 
71 
66 
61 
56 
51 
46 
41 
36 
31 
26 
21 
16 
11 
6 



6 

3 

13 

18 

35 

35 

54 

65 

65 

99 

113 

115 

100 

93 

94 

79 

63 

37 

19 

3 


66 
118 
140 

187 

136 

136 

112 

92 

100 

95 

79 

98 

90 

79 

61 

42 

35 

13 

10 

2 


Total 


1109 


1691 


Median 


43.9 


68.2 



References 

Harlan, Chas. L., "Educational Measurement in The Field of History," Journal oj 
Educational Research, II (December, 1920), 849-853. 

The writer follows a short discussion of tests in the "content" subjects with a brief description 
of his test and its use in nine cities. The requirements he deems essential to a good test are 
listed as a basis of his test. 

Griffith, G. L., " Harlan 's American History Tests in the New Trier Township Schools," 
School Review (November, 1920), 697-708. 

The first half of this article is devoted to a general discussion of history and history testing. 
This is followed by a description of the test and the results of its use in the eighth grade of 
this township. Data are given for each of the single exercises of the test. 



H. Sackett's Scale in United States History 

This scale, arranged by L. W. Sackett, was originally devised by Bell 
and McCollum. It consists of seven tests which appear to have been intended 



30 

for use in secondary schools and colleges. The medians given in Table XVII 
are for the eighth grade. The number of scores is such that it is doubtful if 
the median scores have much value for use as tentative standards. 



TABLE XVII. GRADE NORMS FOR SACKETT'S SCALE IN UNITED STATES 
HISTORY. MAY TESTING. EIGHTH GRADE 





Tests 




I 


II 


III 


IV 


V 


VI 


VII 


Number of pupils 
25-percentile 
Median 
75-percentile 


111 

62.6 
118.7 
192.5 


101 

50.8 

146.2 

273.9 


107 

69.2 

115.0 

183.1 


92 

37.0 

125.0 

287.5 


93 

44.7 

86.5 

193.7 


78 
7.5 
46.6 
138.1 


85 
9.6 
96.5 
195.5 



References 

Bell, J. C. and McCollum, D. F. "A Study of the Attainments of Pupils in United 
States History," Journal of Educational Psychology, VIII (May, 1917), ISl-lA. 
The writers follow a discussion of historical ability with an account of the use of test material 
in various schools from Grade V through the senior year of the University of Texas. The 
results secured are analyzed. The test questions used were in general similar in kind to those 
of Sackett's Scale in Ancient History, although based upon United States History. 

Sackett, L. W. "A Scale in Ancient History." Journal of Educational Psychology y. 
VIII (May, 1917), 284-93. 

The test questions are given with a brief statement of their source, use, and scoring. Results 
are given from almost 1000 papers, and the relative difficulty of the questions computed. 

Sackett, L. W. "A Scale in United States History," Journal of Educational Psy- 
chology, X (September, 1919), 345-348. 

The writer tells of the development of this scale out of the data furnished by Bell and McCol- 
lum 's work referred to above. The determination of the relative difficulty of the parts i& 
given considerable space. 

I. HoTz's First Year Algebra Scale 

This scale consists of five separate scales: (1) Addition and subtraction j. 
(2) Multiplication and division; (3) Equation and formulae; (4) Problems; 
(5) Graphs. Each sub-scale consists ofexercises arranged in order of increasing, 
difficulty. 



References 
Hotz, H. G. First Year Algebra Scales, Teachers College, Columbia University, Contri. 
butions to Education No. 90. 

The writer gives a history of the derivation of these scales, a complete reproduction of them, 
and a discussion of their administration and use. The statistical working out of the scales 
is treated fully for one of them, the procedure for all being the same. 

Cawl, F. R. "Practical Uses of an Algebra Standard Scale," School and Society 
(July, 1919), 89-91. 

The results of testing a class in a large private school are here presented. The matter of 
correlation with English, French, and Latin is considered. A short interpretation of results 
is given, with suggestions as to the value of using such a scale. 



31 



TABLE XVIII. GRADE NORMS FOR 

HOTZ'S FIRST YEAR ALGEBRA 

SCALES. MAY TESTING 





Grade 




IX 


X 


Addition and Subtraction 






Number of pupils 


561 


390 


25-percentile 


5.2 


5.8 


Median 


6.9 


7.3 


75-percentile 


9.1 


8.7 


Multiplication and Division 






Number of Pupils 


570 


388 


25-percentile 


5.7 


5.9 


Median 


7.2 


7.4 


75-percentiIe 


8.4 


8.7 


Equations and Formulas 






Number of Pupils 


478 


385 


25-percentile 


6.2 


6.7 


Median 


7.7 


7.9 


75-percentile 


9.7 


9.1 


Problems 






Number of Pupils 


566 


394 


25-percentile 


4.5 


3.9 


Median 


6.4 


5.0 


75-percentile 


8.6 


6.3 


Graphs 






Number of Pupils 


121 


413 


25-percentile 


5.2 


4.1 


Median 


6.2 


5.0 


75-percentile 


7.0 


6.0 



J. Minnick's Geometry Tests 

This series of tests is based on the assumption that the demonstration 
of a geometrical theorem involves the following abilities: Test A, the ability 
to draw the figure. Test B, the ability to state the hypothesis and conclusion. 
Test C, the ability to recall the facts concerning the figure. Test D, 
the ability to select and organize facts so as to produce the proof. 
Test E, the ability to draw auxiliary lines. The series includes one test for 
each of these abilities. No report is made for Test E. These tests are unique 
in that they provide for both positive scores and negative scores. The positive 
score is the percent of the necessary elements of the proof given correctly by 
the pupil. The negative score is the number of incorrect and unnecessary 
elements. 

References 

Minnick, J. H. An Investigation of Certain Abilities Fundamental to the Study of Geometry, 
University of Pennsylvania, 

This monograph gives a synopsis of methods and results used in deriving the tests, followed 
by a more detailed statement. The latter includes a reproduction of the tests, tables giving 
data secured from testing, statistical methods of weighting exericises, suggestions as to use, etc. 



32 



TABLE XIX. GRADE NORMS FOR MINNICK'S GEOMETRY TESTS 



Test A (ability to draw accurate figures for theorems) 

Number of pupils 

25-percentile 

Median 

75-percentile 
Test B (Ability to state hypothesis and conclusion in 
terms of given figure.) 

Number of Pupils 

25-percentile 

Median 

7S-percentile 
Test C (Ability to recall known facts about figures when 
one or more are given). 

Number of Pupils 

25-percentile 

Median 

75-percentile 
Test D (Ability to organize and select facts to produce a 
proof). 

Number of Pupils 

25-percentile 

Median 

75-percentile 



Positive 


Scores 


Negative 


Scores 


Grade 


Gra 


de 


X 


XI 


X 


XI 


126 


66 


126 


60 


53.3 


43.8 


2.4 


1.1 


63.0 


58.0 


4.1 


2.6 


67.2 


69.2 


6.6 


5.4 


167 


66 


167 


66 


55.2 


55.5 


1.1 


1.0 


69.6 


67.1 


2.3 


2.0 


81.3 


83.6 


3.9 


3.9 


154 


65 


154 


63 


52.2 


55.6 


1.9 


1.4 


64.1 


64.7 


3.8 


3.9 


77.2 


77.9 


7.1 


5.7 


155 


68 


155 


54 


68.0 


75.0 


.8 


.8 


85.5 


89.2 


1.6 


1.6 


92.9 


98.3 


2.3 


3.2 



Minnick, J. H. "A Scale for Measuring Pupil's Ability to Demonstrate Geometrical 
Theorems," School Review, (Feb., 1919), 101-109. 

A brief account of the construction of a scale to measure one definite geometric ability is given. 
The scores made upon the first selection of exercises,' the resultant weighting and then the 
selection of those best suited to make up a scale are briefly treated. The exercises chosen are 
reproduced. 

Minnick, T- H. "Certain Abilities Fundamental to the Study of Geometry," Journal 
of Educational Psychology, (Feb., 1918), 83-90. 

Four abilities requisite to formal geometrical demonstration are listed. Their relation to 
teaching, development by teaching, and diagnosis by tests are discussed. The tests used 
were those of the author. Correlations with teachers marks are given. 



K. Holley's Sentence Vocabulary Scale 
This scale consists of a number of exercises of the following type: 

1. Impolite people are kindly brave young ill-bred. 

2. A man \s afloat \n a mine tower boat hospital. 

The pupil is asked to underline the word which makes the truest sentence. 
These exercises are arranged in order of increasing difficulty, and a pupil's 
score is found by subtracting one-third of the number of errors from the number 
correct. An abbreviated form of this scale has been incorporated in the Illinois 
General Intelligence Scale. The scale was constructed to provide a suitable 
means of ascertaining the general intelligence of groups of children. The 
measure which it yields is not sufficiently accurate to be used as an index of 
the general intelligence of individual pupils. The scale is also recommended as 



33 

an instrument for measuring the vocabulary of pupils. The total distributions 
given in Table XXI indicate that this scale is too difficult for pupils in the 
third and fourth grades. 

TABLE XX. GRADE NORMS FOR HOLLEY'S SENTENCE VOCABULARY SCALE 

APRIL TESTING 













Grade 












III 


IV 


V 


VI 


VII 


VIII 


IX 


X 


XI 


XII 


Number of pupils 
25-percentile 
Median 
75-percenti!e 


406 

8.4 

16.6 

28,5 


520 
16.7 
25.1 
33.6 


465 
25.3 
33.0 
39.9 


450 
33.4 
42.8 
51.5 


1188 
32.3 
41.9 
49.7 


1047 
40.1 

47.7 
55.8 


253 
40.9 
49.0 

57.1 


223 
50.1 
56.0 
63.5 


155 

52.4 
59.9 
67.9 


108 

54.5 
62.7 
70.1 



References 

Terman, L. M. and Childs, H. G. "A Tentative Revision and Extension of the Binet- 
Simon Measuring Scale of Intelligence," Journal of Educational Psychology. (April, 1912) 
205-208. 

The basis of Holley 's Sentence Vocabulary Scales is the Stanford Revi.?ion, 100 word Vocabu- 
lary Test, the construction of which is here described. Tentative standards of achievement 
are also given. 

Holley, C. E. Mental Tests for School Use. Bureau of Educational Research, Uni- 
versity of Illinois, Bulletin No. 4 pp. 86-91. 

This bulletin gives an account of a comparative study of six group intelligence scales, of which 
the above was one, based on data from the school system of Champaign, Illinois. A brief 
account of the origin of the Sentence Vocabulary Scales is included (p. 30). 

Branson, E. P. "An Experiment in Arranging High-School Sections on the Basis 
of General Ability," Journal of Educational Research, (Jan., 1921), 53-56. 
At Long Beach, California, this scale was given to two groups of high-school entrants who had 
recently taken, and been grouped by the Otis Group Intelligence Scale. At the end of the 
term the test was repeated. A comparison by groups oi the scores at the two periods, and 
correlations with the Otis Scale, are given. 



TABLE XXL HOLLEY'S SENTENCE VOCABULARY SCALE 


. GRADE DISTRI- 






BUTIONS FOR APRIL TESTING 










Grade 


















III 


IV 


V 


VI 


VII 


VIII 


IX 


X 


XI 


XII 


90 










6 












80 










5 






1 


2 


7 


70 










3 


1 


8 


21 


27 


21 


60 




1 


5 


50 


75 


126 


32 


56 


48 


36 


50 


31 


4 


20 


74 


199 


321 


79 


85 


52 


31 


40 


18 


44 


89 


141 


379 


341 


78 


45 


23 


13 


30 


42 


128 


170 


110 


290 


153 


50 


15 


3 




20 


71 


170 


137 


59 


123 


73 


5 








10 


124 


130 


30 


13 


74 


29 


1 











120 


43 


14 


3 


34 


3 










Total 


406 


520 


465 


450 


1188 


1047 


253 


223 


155 


108 


Median 


16.7 


25.1 


33.0 


42.8 


41.9 


47.8 


49.0 


56.0 


59.9 


62.7 



34 

L. Holley's Picture Completion Test for Primary Grades 

This test, as it name suggests, consists of a number of pictures which are ■ 
incomplete. The pupil is expected to add the part which is missing. It was 
designed as an instrument for measuring the general intelligence of young 
children. The total distributions as given in Table XXIII indicate that it is 
not a good instrument for this purpose. The distributions exhibit unusually 



TABLE XXII. 



GRADE NORMS FOR HOLLEY'S PICTURE COMPLETION TEST 
FOR PRIMARY GRADES. JANUARY TESTING 





Grade 




Kinder- 
garten 


I 


II 


III 


IV 


Number of pupils 
25-percentile 
Median 
75-percentiIe 


75 
1.8 
5.3 
7.8 


1438 
4.4 
7.8 
12.2 


1233 
7.9 
11.5 
15.1 


327 
9.9 
13.5 
16.5 


167 
8.8 
12.3 
15.0 



TABLE XXIII. HOLLEY'S PICTURE 
COMPLETION TEST FOR PRIMARY 
GRADES. GRADE DISTRIBU- 
TIONS FOR JANUARY . 
TESTING 







Grade 




Score 








I 


II 


III 


IV 


20 


34 


31 


9 


4 


19 


23 


43 


13 


4 


18 


33 


46 


25 


9 


17 


36 


59 


20 


12 


16 


42 


64 


27 


3 


15 


52 


72 


34 


10 


14 


47 


76 


22 


15 


13 


54 


88 


26 


14 


12 


48 


98 


24 


17 


11 


82 


77 


19 


14 


10 


72 


92 


24 


9 


9 


81 


84 


24 


12 


8 


9] 


89 


26 


9 


7 


103 


75 


11 


11 


6 


122 


59 


9 


13 


5 


94 


50 


8 


8 


4 


112 


50 


4 


2 


3 


108 


29 


1 


1 


2 


86 


21 


1 




1 


77 


28 









41 


2 






Total 


1438 


1233 


327 


167 


Median 


7.8 


11.5 


13.5 


12.3 



35 



high variability. This is much greater than is exhibited by other tests when 
applied to children in these grades. The median scores given in Table XXII 
give further indications of the inadequacy of this test, particularly in the grades 
above the first. 

References 

Holley, C. E. Mental Tests for School Use. Bureau of Educational Research, University 
of Illinois, Bulletin No. 4, pp. 86-91. 

A general discussion of tests of this type is followed by an account of the testing from which 
this test came. This was done in Champaign, Illinois. Results are merely outlined. 



CHAPTER III 

THE DERIVATION OF MONROE's STANDARDIZED REASONING 
TESTS IN ARITHMATIC^ 

The process of problem solving." Reasoning"asit occurs in the solving 
of an arithmetical problem involves these steps: (1) A careful reading of the 
problem including the association of correct arithmetical meanings with the 
"technical" terms used in stating the problem. (2) Recall of facts and prin- 
ciples suggested by the problem and required for its solution. (3) Formulation 
of a hypothesis or plan of solution using as data the results of the first two steps. 
(4) Verification of this plan of solution. This process of reasoning is usually 
followed by the calculations outlined in the plan of solution. This additional 
step, however, is not a part of the reasoning process. 

Two kinds of words are used in stating arithmetical problems: (1) 
The descriptive words give the setting of the problem. Only in an indirect 
way do these affect the solution. (2) The "technical terms" of an arithmetical 
problem consist of those words and phrases which define quantities and quan- 
titative relationships. Every problem involves at least three quantities, 
two given and the third to be found. These quantities are related in a definite 
way. For example, the sum of the two quantities given equals the third, or 
the third is the quotient of one divided by the other. In problems involving 
two or more steps there are more than three quantities and the relationships 
are more complex. However, in every case there are words or phrases which 
either directly or indirectly tell what these relationships are, and, consequently, 
what operations must be performed to obtain the desired answer. 

This principle may be illustrated by the following problems: "What 
are the average daily earnings of a boy who receives $0.88, $0.25, $1.15, $0.75, 
$0.50, and $0.60 in one week?" 

The phrase "average daily earnings" names the quantity to be found 
and also specifies its relationship with the given quantities. The "average" is 
the quotient of the sum of the several amounts divided by the number of items. 
A knowledge of this definite meaning of "average" is necessary if one is form- 
ulating a rational plan of solving the problem. If the phrase "average daily" 
was omitted we would have an entirely different problem. 

"How many square yards of linoleum will be required to cover a floor 
16 feet by 12 feet?" 

"How many square yards" names the third quantity in this problem 
and in connection with " 15 feet by 12 feet" specifies the relations which exist 



*A number of considerations on which the derivation of these tests is based are con- 
tained in an article by the writer in School and Society, Volume VIII, pages 295 and 424. 
Sample copies of these tests may be obtained from the Public School Publishing Company, 
Bloomington, Illinois. 



37 

between the quantities. This third quantity is the product of the dimensions 
divided by nine.^ In this case the number of square feet in a square yard must 
be remembered and also the principle that the area of a rectangle (i.e., a figure 
whose dimensions are given as in the problem) is the product of the length by 
the width. 

In many cases when the first two steps of the reasoning process have 
been completed satisfactorily, the formulation of the plan of solution (the next 
step in the reasoning process) involves little uncertainty. In fact it is essentially 
mechanical. This is the case in these illustrations. In the case of very simple 
problems, or very familiar problems, the reasoning process is usually short- 
circuited so that there is no explicit association of meaning with the technical 
terms nor recall of principles. The problem as a whole or some feature of it 
serves as a cue for the direct association of the plan of solution. In such cases 
there is strictly speaking, no reflective thinking or reasoning, and the mental 
process involved is much the same as that which occurs in the operations of 
arithmetic. The solution of the problem has become automatic. 

The nature of a reasoning test in arithmetic. A reasoning test in 
arithmetic is essentially a test of careful reading in a limited field to answer 
specific questions. In this reading, technical vocabulary is fundamental. 
The pupil gives evidence of his degree of comprehension by his plan of solution. 
The correctness of the numerical answer to the problem depends upon the ac- 
curacy of the pupil 's calculations and the recall of denominate number facts 
as well as upon the plan of solution. The plan, or principle, of the solution 
and not the accuracy of the numerical answer is, therefore, the measure of the 
pupil's ability to reason in arithmetic. Thus in describing a pupil's perform- 
ance on a reasoning test, errors in the recall of facts and in calculation should 
be disregarded. For the problems which are solved correctly in principle a 
score based on correct answers may be used as a crude measure of the pupil 's 
ability to perform the operations of arithmetic. 

In order that a pupil's score on a reasoning test may be indicative of 
his ability to solve arithmetical problems in general, the problems must be 
carefully selected with reference to content (vocabulary). The ideal reasoning 
test would be one that included all of the technical terms but this is not possible 
because the vocabulary of arithmetical problems is extremely varied and volum- 
inous. In another^ place the writer has reproduced 28 different forms of state- 
ment which were found in the examination of eight text-books for the problem, 
"Given, $7.50, paid for silk, and price per yard ?1.50, to find the number of 
yards purchased." This condition makes it necessary to select a few problems 
which will be representative in respect to content, in order to have a test of 
usable length. 



'An alternative solution is to reduce each dimension to yards before finding the area. 
*Monroe, Walter S. Measuring the Results of Teaching, Houghton Mifflin Company 
(1918), 163. 



3S 

Method of selecting problems on basis of content. In the case of the 
series of tests described in this report the representative problems were selected 
by the following method. The one- and two-step problems appearing in eight 
widely used texts were classified according to the operation or operations they 
called for. This gave in one group all the problems requiring only addition, 
in another those requiring only subtraction and so on. The problems in each 
of these groups were further classified by the writer on the basis of the technical 
terms used. This was found to be difficult because of the great variety of 
these terms. Since the classification represents the judgment of only one person, 
it cannot be considered final in any sense. 

The general plan of classification may be illustrated by the types of 
division problems. In the list on the following pages only those types are given 
which included problems found in five or more of the eight texts examined. 
A large number of additional types included problems from less than a majority 
of the texts. A descriptive statement of the type is followed by a limited 
number of illustrative problems. It will be noted that for a single type these 
problems are not identical in vocabulary but it was the judgment of the 
writer that they were sufficiently similar to justify grouping them together. 
It has been assumed that the terms used are essentially synonymous. This 
hypothesis is, of course, subject to experimental verification. Unfortunate- 
ly, this is lacking at this time. However, the resulting list of type prob- 
lems is more representative of the vocabulary of arithmetical problems as they 
occur in our texts than any other available list. 

Description of types and illustrative problems: 

1. Given a whole to find number of parts of a given size, including 
to find the number of acres to produce a given yield. 

A baker used three-fifths lbs. of flour to a loaf of bread. How many loaves 
could he make from a barrel? 

When the average yield per acre is 25 bushels how many acres will yield 925 
bushels. 

How many lengths three-fourths yds. long can be cut from 15 yds. of goods? 

How many hens can be properly accommodated in a pen containing 51 square 
feet, if each hen requires 6 square feet? 

964 marbles are distributed equally among a certain number of boys. Each 
boy has 82 marbles. How many boys are there? 

At 7}4 gallons to the cubic foot, how many cubic feet will 3000 gallons of 
oil occupy? 

Oats weigh 32 lbs. to a bushel. How many bushels are there in a load weigh- 
ing 1344 lbs? 

2. Given cost and price to find the number of articles purchased. This 
includes wages when question is how many days, weeks, etc. to earn 
a given amount. 

At 16 cents per pound, how many pounds of steak does a woman get it the 
amount of the purchase is 80 cents. 



39 

3. The reverse of No. 1. Given whole and number of parts to find 
size of each part. 

Three boys buy a rowboat for twelve dollars and seventy-five cents, sharing 
the expense equally. Find how much each boy has to pay. 

If 54 marbles are divided equally among 6 boys, how many marbles will each 
receive ? 

In 28 days a hotel used 361 lbs. of butter. How many pounds did it use a day? 

4. The reverse of No. 2. 

A farmer paid thirty-three dollars and a half for 4 bushels of seed wheat. How 
much did he pay for a bushel? 

The bill for 58 tons of copper amounted to 612 dollars. What was the price 
per ton? 

A fowl weighing 4 and one half lbs. sells for 51.00. What is the price per pound? 

A man's wages amounted to 46 dollars for 9 and one-fifth day's work. How 
much did he receive per day? 

A man works 8 hours a day for 4 dollars and 80 cents. How much does he 
receive for each hour's work? 

-5. Given the price for a given denomination to find the price at a lower 
denomination. 

A boy bought a dozen oranges at the rate of 15 cents a dozen. W'hat did they 
cost him apiece? 

When milk is 10 cents a q,uart, how much is a pint worth? 

6. Given the whole and the number of parts to find the average (rate, 
price, yield, etc.) 

A farmer raised 500 bushels of wheat on a field of 40 acres. What was the 
average yield per acre? 

A fast train runs from Chicago to a station 356.4 mi. distant in exactly 9 hours. 
What is the average rate of the train? 

A drover paid J1125 for cows, what was the average price if he bought 25? 
A mill employs 600 hands and has a weekly pay roll of $2,000. What is the 
average weekly wage for each employee? 

7. The whole and the rate are given. The question is asked by, "How 
long?" 

If a horse eats three-eights bu. of oats a day, how long will 6 bus. last? 
How long will it take to earn 28 dollars at $1.75 a day? 

■8. Given distance and rate to find how long. 

At 25 miles an hour, how long will it take an automobile to go 160 miles? 

9. Given distance and number of units of time to find ratel 

In 3.2 hours a man walks 12.32 mi. How far does he walk in one hour? 

Find the rate of speed per hour made by an airship traveling 218.05 miles in 
3.5 hour. 

10. A fractional part of a whole is given to find the whole. 

If, when 18 and three eighths mi. of track are laid, one third of the road is 
completed, how long is the road? 

I sold a bicycle for 18 dollars. This was three sevenths of what I paid for it. 
How much did I pay for it ."^ 



40 • 

11. A percent of the whole is given to find the whole. 

If 33 and one third percent of a man's loss is 300 dollars, how much does he- 
lose ? 

A girl spent 25 cents which was 12>^ percent of her monthly allowance, how 
much was her allowance? 

A clerk had his weekly wages increased 3 dollars, or 16 and two thirds percent. 
What were his wages before this increase? 

12. Given the amount of gain or profit and percent of gain or profit to 
find the cost or selling price. 

A hardware merchant makes a profit of 25 percent or 32 cents on saws. Find; 
the cost. 

A farmer sold his horse at a gain of 30 dollars, or 25 percent. Find the cost. 

13. Given the commission and percent of commission to find amount 
sold. 

Five percent commission on a certain amount of money was 684.20 dollars. 
What was the amount? 

14. Given two numbers to find what percent one is of the other. 

If 1000 lbs. of potatoes contain 180 lbs. of starch, what percent of potatoes is- 
starch? 

If a man saves 187.50 dollars out of his salary of 1250 dollars, what percent 
does he save? 

The boys in the Marshall school won 5 of the 8 games of hockey. What percent ? 

In his examination in arithmetic a boy had 10 problems out of twelve rights 
His grade was what percent? 

15. Given two numbers to find what part one is to the other. 

The Jackson basket-ball team won 35 out of 56 games. What part did it win? 

A man spends for rent 360 dollars out of an income of 1 500 dollars. What part 
of his income is spent this way? 

16. Given the amount of investment, or principle, and the income or 
interest to find rate. 

Mrs. Lynch received 24 dollars a year interest on 400 dollars loaned Mrs.. 
Burnet. What is the rate? 

17. Given an amount in one denomination to reduce to a higher. 

An aviator reaches a height of 11,474 feet. Express this height in miles. 

A milk dealer sells 302 qts. of cream. Express this as gallons and quarts. 

In digging out a cellar 8260 cubic feet of earth were removed. At 27 cubic: 
feet to the cubic yard, how many cubic yds. were removed? 

18. Given the value or face of a policy and premium to find the rate. 

Find the rate, given the face of the policy as 1500 dollars and premium 15- 
dollars. 

A fire insurance company charged 20 dollars for insuring an automobile for 
1000 dollars. What was the rate of insurance. 



41 



19. Given the premium and rate of insurance to find face of policy. 



A man paid 50 dollars tor insuring a house, the rate being 2 and 
What was the face of the policy? 



'A percent. 



Table XXIV gives the frequency of occurrence of each type in each of 
the eight texts examined. This table is to be read as follows: 10 problems 
classified as belonging to Type 1 which were found in Text 1; 30 such prob- 
lems were found in Text 2; 20 in Text 3; 34 in Text 4, etc. The total number 
of problems classified under Type 1 is 147. 

The variations in the frequency of the occurrence of problems belonging 
to a single type are worthy of notice. Some types have a high frequency in 
certain texts while in other texts their frequency is low and in many cases 
they do not occur at all. This means that different authors have tended to 
use different vocabularies. 



TABLE XXIV. FREQUENCY OF OCCURRENCE OF TYPES OF PROBLEMS 
IN DIVISION IN EIGHT TEXTS 













Text 








T V PF ?CtTV1RFR 




















1. irH' i^UiViiict^ 


1 


2 


3 


4 


5 


6 


7 


8 


Total 


1 


10 


30 


20 


34 


8 


13 


13 


19 


147 


2 


28 


14 


123 


11 


- 


75 


49 


27 


327 


3 


_ 


7 


6 


2 


4 


11 


3 


15 


48 


4 


11 


24 


24 


2 


19 


20 


14 


17 


131 


5 


2 


4 


2 


- 


3 


1 


- 


1 


13 


6 


5 


10 


4 


9 


3 


13 


4 


52 


100 


7 


_ 


2 


2 


3 


2 


1 


1 


2 


13 


8 


1 


1 


- 


4 


- 


4 


1 


- 


11 


9 


2 


7 


3 


- 


1 


1 


2 


12 


28 


10 


_ 


1 


13 


2 


2 


13 


3 


2 


36 


11 


6 


19 


13 


3 


- 


4 


11 


16 


72 


12 


1 


- 


2 


- 


1 


1 


3 


- 


8 


13 


_ 


1 


1 


2 


4 


1 


- 


1 


10 


14 


9 


42 


12 


41 


3 


14 


39 


30 


190 


15 




12 


5 


- 


1 


- 


18 


4 


40 


16 


1 


2 


1 


1 


1 


8 


1 


8 


23 


17 


6 


1 


1 


1 


- 


2 


2 


- 


13 


18 


8 




4 


- 


1 


- 


3 


7 


23 


19 


9 


- 


3 


1 


- 


- 


1 


1 


15 



Space does not permit the reproduction of similar tables for addition, 
subtraction, multiplication and the classes of two-step problems. In Table 
XXV a summary of the frequencies of the occurrence of the several types is 
given. This table is read as follows: In the case of problems requiring only 
addition, three types occurred in all eight texts, one occurred in seven and two 
in six texts. The total number of types occurring in five or more of the texts 
is six. The total number of problems classified in these six types is 464. The 
total number of problems is 622. 

The reader should bear in mind thait no attempt was made in this classi- 
fication to determine what problems pupils should be asked to solve. The 



42 

problems have been taken as they occurred in the texts. In effecting the classi- 
fication, no consideration was given to the question of whether the problem 
was practical. In fact the purpose was not to obtain a list of practical problems 
but to secure a list of the forms of statement or language which had been used 
in the one- and two-step problems by the authors of widely used texts. Many 
of the technical terms of arithmetic are used (probably must be used) whether 
the problems are practical or not. 

Experimental selection of problems. In order to secure data for 
the construction of a series of reasoning tests in arithmetic, about 300 problems 
were selected out of the total number examined and classified. Out of this num- 
ber 156 problems were chosen for an experimental series of tests. In making 
the selections for this purpose the writer considered, in addition to the classifi- 
cation described above, the social importance of the problems. Thus a few 
types of problems which occur in a majority of the texts and have a high total 
frequency, were not represented. This introduces an additional subjective 
factor but in view of the emphasis which is being placed upon the social im- 
portance of the subject matter, the writer believes it is better to exercise judg- 
ment in this instance rather than to follow blindly statistics based upon the 
content of our present texts, particularly when it is obviously impossible to 
include representative problems of all types within a single series of tests of 
suitable length for classroom use. 

TABLE XXV. FREQUENCY OF TYPES OF PROBLEMS 





Number of types 










OCCURRING IN 


Total 


Frequency 


Frequency 


Operation 




No. of 


OF problems 


OF ALL 














8 


7 


6 


5 


Types 


CLASSIFIED 


Problems 




texts 


texts 


texts 


texts 








+ 


3 


1 


2 





6 


464 


622 




1 


2 


4 





7 


211 


456 


X 


5 


5 


2 


3 


16 


1641 


1938 




5 


6 


3 


5 


19 


1248 


1610 


+ - 


1 


2 


2 




5 


199 


346 


+x 


4 


2 


3 


4 


13 


472 


718 


+-^ 


1 





1 


3 


5 


127 


299 


-X 








1 


7 


8 


166 


559 


■- 


1 





3 




4 


114 


413 


XX 


3 


1 


2 


4 


10 


429 


581 


XH- 


1 


4 


2 


6 


13 


704 


1234 


++ 














7 


-j--^ 














70 


Total 


25 


23 


25 


32 


105 


5775 


8853 



In constructing the experimental series, Test I was designed for grades 
four and five. Test II for grades six and seven, and Test III for grade eight. 
Some such division is necessary because certain social situations from which. 



43 

problems are taken are not studied until the later grades although the 
mathematical relationships are very simple. Pupils cannot be expected to solve 
such problems until they are acquainted with the social situations. For 
this reason all problems involving percentage were placed in Test III. No 
consideration was given to the relative difficulty of the problems in making 
this division except that no problems requiring common fractions were placed 
in Test I and for the most part decimal fractions were confined to Test III. 

Each test consisted of sixteen problems printed on a four page folder 
with space so that the pupil could do all of his work upon the test paper. The 
test papers showed that unless the pupil made errors and did his work over or 
used an elaborate method, ample space was provided except in a very few 
cases. The directions for administering the preliminary tests were essentially 
the same as those which now accompany the tests. 

A number of cities were invited to cooperate by giving the tests between 
April 1 and 15, 1918. Fourteen cities respxjnded, nine in Kansas, and one 
city in each of the following states: Illinois, Ohio, Michigan, New York, and 
Pennsylvania. Usable returns were received from 12,859 pupils. 

When the record sheets and the test papers were returned to the writer 
it was found that the directions for marking the papers were not sufficiently 
complete and explicit. Consequently, there was a lack of uniformity in the 
marking. In order to insure uniformity the writer, assisted by two clerks 
rescored the papers. Whenever an unusual or questionable solution was 
found a record was made and all similar solutions were marked in the same way. 
In this way a high degree of uniformity in the marking of the papers was secured. 
Space does not permit a detailed statement of the plan of scoring of the solution 
of each problem but the general plan may be indicated. 

The solution of a problem was considered correct in principle if the 
pupil's work showed that he had based his solution upon the relationships 
which exist between the quantities of the problem. For example, in the 
problem, "If a man has $275 in the bank and draws out 370, how much has he 
left in the bank?", there are three quantities: $275, $70, and the amount 
"left in the bank." These are related so that the difference between $275 
and $70 must equal the amount left in the bank. A solution of the problem 
based upon this relationship must involve the subtraction of $70 from $275, 
or the finding of a number which added to $70 will make $275. 

In the problem, "A house rents for $35 a month. This is how much a 
year?", the three quantities are $25, 12, or the number of months in a year, 
and the amount for a year. The relation is that the product of $35 and 12 
equals the amount of rent for a year. A solution based upon this relationship 
would usually be one in which $35 was multiplied by 12. In a few cases the 
pupil had set down $35 twelve times and added. This solution was counted 
as correct in principle because it was considered that the pupil had recognized 



44 

the relationship which existed between the quantities ot the problem. Inci- 
dentally it should be noted that although such a solution was counted as being 
correct in scoring the papers of the test, a teacher should not encourage it. 
In fact the writer believes it should be discouraged, except possibly when the 
pupil is learning the idea of multiplication, because the method is not efficient. 
It requires more time and there are more opportunities for error in the mech- 
anical work. 

In the case of the above problem, if a multiplier other than 12 was used the 
solution was counted as correct in principle because it was considered that 
correct recall of denominate number facts was not a part of the reasoning. 
In a few cases 35 was multiplied by itself. This was marked incorrect in 
principle. 

Although the pupils were directed to do all work upon the test papers 
a few gave only the answer in the case of certain problems. They had either 
solved the problem mentally or on another sheet of paper. An arbitrary rule 
was adopted. If the answer was correct the problem was marked correct in 
principle and answer. If the answer was wrong it was marked incorrect in 
both principle and answer. 

An answer was not marked correct unless the solution of the problem 
was correct in principle and the answer was numerically correct and in its 
lowest terms if it contained a fraction. It was not required that the answer 
be labeled with its denomination. 

Weighting the problems. For each problem three records were secured : 
(1) Number of pupils attempting the problem. (2) Number of solutions 
correct in principle. (3) Number of correct answers. From these facts the 
percent of solutions correct in principle and the percent of those solved accord- 
ing to the right principle which had also correct answers were calculated. These 
percents were translated into sigma values. The former being designated as 
the "P" value of the problem and the latter as the **C" value. In doing this 
it was assumed that the ability to solve problems was distributed normally 
and included between +2.5 sigma and — 2.5 sigma. The tables given in Rugg's 
"Statistical Methods as Applied to Education" were used. The values 
were calculated to two decimal places but in order to simplify the computation 
of scores they were expressed in terms of the nearest integer in the tests as now 
published. 

In the case of those problems which were solved by the pupils in two 
successive grades, the average inter-grade interval was found for each group of 
problems by taking the average of the differences of the sigma values of the 
problems of the test. This inter-grade interval was added to the values of 
the problems for the upper of the two grades to reduce them to the basis of the 
lower grade. The average of the two values was taken as the final value of 
the problem. 



45 

An attempt was made to reduce the sigma values to a common zero 
point, and thus secure comparable scores, by having a limited number of prob- 
lems from Test I appear in Test II and also a limited number of problems from 
Test II appear in Test III. It happened that some of the problems chosen 
showed inversion and for this reason it was deemed advisable not to attempt to 
reduce the values to a common zero. Thus the scores obtained from the differ- 
ent tests of the series are not comparable.' 

Construction of the final tests. Out of the 156 problems included 
in the preliminary test, 90 which belonged to types occurring in five or more of 
the eight texts examined, were selected for the final tests. Since in the select- 
ion on the basis of content there was no effort to include problems which ex- 
hibited wide range of difficulty, there was no attempt to construct a difficulty 
scale. In fact it is the judgment of the writer that the educational objectives 
implied by such a scale in the field of problem-solving are open to serious 
criticism. In our schools we should endeavor to instruct pupils to solve 
problems because they are socially worth while rather than because they exhibit 
a certain degree of difficulty. The purpose here is to construct a group of 
tests containing problems that are representative of the language in which 
problems are stated in our representative text books and which appear to be 
satisfactory for testing purposes. 

The final tests consist of 15 problems each. Test I is for grades four 
and five, Test II for grades six and seven, and Test III for grade eight. There 
are two forms of each test. In selecting the 90 problems for these tests those 
were rejected which were commented on unfavorably by those who gave the 
preliminary tests. Also those problems were rejected which were found to be 
particularly confusing to pupils. The arrangement of the order of the problems 
in a test was made without reference to their difficulty values. An attempt 
was made to secure as high degree of variation in the operations required as 
possible. In the two forms of each test the corresponding problems are ap- 
proximately equal in difficulty, and so far as possible, the two forms were made 
equivalent in other respects.^ 



'The method of weighting is open to criticism. It is used in an attempt to give more 
credit for doing a difficult problem than for doing an easy one. It is not at al! certain that 
such a plan gives the most truthful indication of a pupil's ability. Some recent studies 
have shown that unweighted scores correlate very highly with the weighted scores obtained 
by this method. Therefore, it is likely that the tests would have been nearly as accurate 
measuring instruments without any determination of weights. 

*No determination of the reliability or validity of these tests was made as a part of the 
original derivation. Neither is it possible to make a report on these questions at this time. 
Some work which was done on the question of reliability indicated that the tests were less 
reliable than tests in the operations of arithmetic and in silent reading. This appeared to 
be due to the fact that frequently pupils are unable to do certain problems because of a 
peculiar course of study. 



46 

Analysis of errors made by pupils on preliminary test. In the pre- 
liminary testing the following six problems were given to 100 fifth grade 
pupils in one city. The results of an analysis of the test papers are given 
in Table XXVI. 

1. Mrs. Black received $2 a yd. for broadcloth. She sold 78 yds. How much did she 
receive ? 

2. At the store a towel roller costs 35c. George made one for his mother. He used 
12c v/orth of lumber, 2c of hardware, and 3c worth of shellac. Find how much George saved 
his mother. 

3. A Kansas farmer bought 80 acres of cheap land for $240. Oil being found on his 
farm he sold the land for $60,000. What was his profit? 

4. A car contains 72,060 lbs. of wheat. How much is it worth at 87c a bushel? 

5. _A field is 20 rds. long and 12 rds. wide. How many rods of fence are needed to 
enclose it? 

6. What are the average daily earnings of a boy who received 88 cents, 25 cents, $1.15, 
75 cents, 50 cents, and 60 cents in one week? 



TABLE XXVI. RESULTS OF ANALYZING THE ERRORS OF 100 FIFTH GRADE 

PUPILS 





Problem 




1 


2 


3 


4 


5 


6 


Total 


Number of pupils attem.pting 
Errors in reasoning 
Errors in fundamentals 
Omissions and errors in copying 
Errors in decimals 


100 

8 

1 

2 

13 


100 
21 

7 

I 


92 
39 
26 
2 
16 


52 

38 

16 

3 

25 


94 

33 
2 




94 
67 
35 
4 
14 


532 

206 

87 

11 

68 



Two significant facts are shown in this table. First, a majority of the 
errors (55 percent) are in reasoning. More than one-third of the attempts 
(39 percent) resulted in faulty reasoning. Second, 41 percent of the errors 
in calculation were in placing the decimal point. This second fact becomes more 
significant when we note that these errors occurred in problems involving only 
United States money and that the first and third problems which produced 
29 of the 68 errors do not really involve decimal fractions. In these two 
problems the error consisted in pointing off the answer when it should not 
have been done. 

The wide spread use of the Courtis Standard Research Tests, Series B 
and other tests upon fundamentals has resulted in increased attention to the 
fundamental operations with integers. There should be no decrease in the 
emphasis upon this phase of arithmetic for one out of six pupils made errors 
in the simple calculations required in these problems but the greatest source 
of error and therefore the greatest need is increased attention to the mental 
processes involved in reasoning as it occurs in solving arithmetical problems. 
The necessity for doing this becomes more obvious when we examine the nature 



47 

of the errors in reasoning. In problem 2, 13 of the 21 errors in reasoning were 
due to adding all of the terms; in problem 4, 33 out of 38 of the errors in reason- 
ing were due to multiplying 72,060 by 87 without attempting to reduce the 
pounds to bushels; in problem 6, 58 of the 67 pupils who reasoned incorrectly 
simply added the terms. Each of these errors may be ascribed to inaccurate 
or incomplete reading of the problem, or the first step in the rational solution 
of a problem. 

In tabulating the scores of the preliminary test the variation in achieve- 
ment of different classes was particularly noticeable. It was evident that 
some teachers were teaching their pupils to solve problems while others, fre- 
quently within the same school system, were not doing so. It is also sig- 
nificant that a number of teachers consistently marked as correct, solutions 
which were clearly incorrect. This may have been accidental on the part of 
the teacher but this is very doubtful. A striking illustration was furnished by 
the problem: "A baker used 2/S lbs. of flour to a loaf of bread. How many 
loaves could he make from a barrel (1^6 lbs.) of flour?" The correct solution 
requires that 196 be divided by 3/5 which gives an answer of 326 2/3 loaves. 
In several instances teachers marked as correct all papers in a class in which 
196 was multiplied by 3/5. This latter solution gives an answer of 117 3/5 
loaves. The fact that teachers made such errors as this indicates that they 
are not familiar with solving reasoning problems. Perhaps this is one source 
of the poor records made by the pupils. 



CHAPTER IV 

Monroe's timed sentence spelling tests and pupil's errors 

How ability in spelling should be measured. In measuring ability 
in spelling by having a pupil spell words which are dictated in lists it is clear 
that the conditions under which the pupil spells the words are not the conditions 
under which he spells the words which he uses in writing themes, letters, and 
other school exercises. As a result we probably fail to obtain a measure of 
his "true spelling ability." 

If the test words are embedded in sentences and the sentences written 
from dictation we approach more nearly normal spelling conditions because 
the pupil is writing connected words which have meaning. A still closer 
approximation appears to be secured by dictating the sentences at approx- 
imately the rate at which the pupil is accustomed to write. By thus causing 
the pupil to write at approximately his normal rate of writing, he does not have 
time to study over the spelling of words, and as a result we secure a record of 
spelling which is largely automatic. Under such conditions a pupil 's attention 
is centered primarily upon writing and not upon his spelling. Of course, 
these conditions are not those under which the pupil normally spells words^ 
The writing from dictation may be an unusual exercise for the pupil. Some 
pupils will be accustomed to write more slowly than the rate of dictation. 
This may tend to confuse them. To what extent these and possibly other 
factors prevent our obtaining a record of the "true spelling ability" of the 
pupil by a timed-dictation test we do not know. It appears, however, 
that a Timed Sentence Spelling Test is likely to yield a more valid measure of 
spelling ability than a list of words dictated separately. 

The construction of Monroe's Timed Sentence Spelling Tests. 
In order to make easily available a timed sentence spelling test, the writer 
constructed a series of such tests, using test words chosen from appropriate 
columns of Ayres' Scale for Measuring the Ability in Spelling and basing 
the rate of dictation upon the measurements of the rate of handwriting of over 
six thousand Kansas school children. In order that the scores might have a 
high degree of reliability as measures of the spelling ability of individual 
pupils, fifty test words were used in each test. According to one study^ the 
probable error of an individual score for a test of fifty words is less than 1 .00 
when the score is expressed as the percent of words spelled correctly. For a 
class of twenty-five or more pupils the probable error of the class score would 
be 0.2. 



"Otis, A. S. "The reliability of spelling scales involving a 'deviation formula' for cor- 
relation." School and Society, 4, (November 11, 1916), 716-22. This study deals with the 
reliability of tests consisting of isolated words and it is possible that the results might not 
apply to a timed sentence spelling test. 



49 

For grades III and IV the test words were taken from Column M of 
Ayres' Scale for Measuring Ability in Spelling. For grades V and VI they 
were taken from Column Q and for Grades VII and VIII and the high school 
they were taken from Coulmans S, T, and U. The test for the fifth grade is 
reproduced. The sentences are to be dictated when the second hand of the 
watch reaches the position indicated in the left-hand margin. 

In this test no test words come at the end of the sentences. Thus, the 
pupil who writes slowly will be much less likely to make low scores because he 
does not have time to complete writing the sentences. It should also 
be noted that all other words found in these sentences are easier to spell as 
shown by the Ayres Scale. It was thought advisable to allow time for dic- 
tating the sentences in addition to the actual writing. For this reason, the 
rate of writing for each school grade was increased by ten percent, sixty-six 
seconds instead of sixty being allowed for the number of letters which pupils 
commonly write in sixty seconds. 

Tentative grade Norms. This series of timed sentence spelling tests 
was given in sixteen Kansas cities in April and May, 1917. During the school 
year of 1919-20 scores were reported from a number of cities. The grade medians 
for these two groups of cities and the norms given by Ayres are given in Table 
XXVII. In comparing the successive grades it must be remembered that the 
same test words were not used for all grades. One list of test words was used 
for grades III and IV, another for grades V and VI and still another for grades 
VII and VIII and for the high school. 

The fact that the median scores in Table XXVII are materially below 
Ayres ' norms indicates that a different type of spelling ability has been measured 
by the timed spelling sentence test than that measured by Ayres In constucting 
his scale. (Ayres had the words dictated in lists). This fact becomes more 
apparent when it is recalled that many of the cities which gave these tests 
had used Ayres' Scale as a minimum course of study as well as a source of tCgt 
words. Thus, had the test words been dictated in lists it is likely that the m 
ian scores would have been materially above Ayres' norms.'" 

Monroe's Timed Sentence Spelling Test Arranged for the Fifth Grade. 
Seconds 

60 The president gave important information to the men. 

48 The women were present at the time. 
19 The entire region was burned over. 

49 The gentlemen declare the result was printed. 
30 Suppose a special attempt is made. 



'''It is possible that the difference between the median scores and Ayres' norms may be 
due to factors other than the measurement of different types of spelling ability. Many of 
the pupils probably were not accustomed to writing from dictation and all were not accustomed 
to writing at the rate at which these tests were dictated. It is possible that these unusual 
conditions may have been operated to materially lower the scores ot a number ot pupils 
or even of most pupils. 



50 



60 The final debates were held. 
24 Tht factory employs forty men. 

51 Sometimes the connection is not made. 

24 I enclose a written statement with the book. 
3 Prompt action is needed. 

25 It was a wonderful surprise to all. 

55 The addition to the property was begun. 

31 Remember y Saturday is the day. 

57 They <awa// M«V leader. 

19 Either make another f^or/ or return. 

52 The famous estate is close. 

16 In this section little progress was made. 

53 The measure is ^w^ to pass. 
16 A position in the field is his. 

42 To whom was the command given? 

8 Whose claim was bought? 
29 He represents the firm in this matter. 

2 Go forward in that direction to reach the city. 



When the second hand reaches 43, stop the writing. 

Allow no corrections or additions to be made. Ask the pupils to turn their papers over 
and write their name and grade. Appoint two or three pupils to collect the papers. 



TABLE XXVII. MEDIAN SCORES (WORDS SPELLED CORRECTLY) AND 
AYRES ' NORMS. TOTAL WORDS IN EACH TEST IS FIFTY 





Grade 




III 


IV 


V 


VI 


VII 


VIII 


IX 


X 


XI 


XII 


1917 Testing 






















Number of pupils 


1342 


1539 


1427 


1338 


1136 


876 


289 


251 


188 


96 


Median (May) 


28.6 


39.4 


32.8 


41.8 


35.1 


43.0 


43.3 


45.1 


46.5 


47.9 


1919-20 Testing 






















Number of pupils 


437 


423 


440 


302 


218 


153 










Median 


28.2 


43.0 


39.7 


43,0 


32.6 


38.8 










Ayres Norms 


33.0 


42.0 


36.5 


42.0 


39.0 


44.0 











In Table XXVIII the distributions of the scores are given for grades 
III to VIII inclusive. In the fourth, sixth, and eighth grades there are a 
number of perfect scores which show that the test was not sufficiently difficult 
for the best spellers in these grades and, therefore, did not give us a measure 
of their spelling ability. This statement probably applies also to those pupils 
who spelled incorrectly one, two, or three words. From the standpoint of 
accurate measurement of the spelling ability of "good spellers," these tests 
are too easy, especially for grades four, six, and eight and the high school. 

This table is also significant in another respect. The range in the number 
of words spelled correctly extends from zero, or at the most two, up to fifty 
and, as has been pointed out in the above paragraph, the spelling ability of 
some pupils probably extends beyond perfect scores on these tests. That the 



51 



TABLE XXVIII. DISTRIBUTION OF SPELLING 

SCORES ON MONROE'S TIMED SENTENCE 

SPELLING TESTS 









Grade 






Score 














III 


IV 


V 


VI 


VII 


VIII 


50 


7 


45 


13 


40 


14 


33 


49 


11 


53 


23 


83 


21 


48 


48 


13 


82 


29 


75 


31 


64 


47 


17 


76 


44 


81 


45 


60 


46 


24 


83 


30 


82 


40 


55 


45 


28 


89 


38 


77 


38 


61 


44 


17 


63 


50 


78 


39 


59 


43 


34 


64 


38 


81 


54 


59 


42 


36 


58 


49 


60 


34 


48 


41 


37 


45 


49 


62 


30 


40 


40 


35 


76 


55 


69 


37 


33 


39 


39 


57 


31 


47 


40 


25 


38 


29 


67 


35 


48 


34 


29 


37 


30 


42 


55 


43 


30 


28 


36 


43 


53 


44 


34 


44 


17 


35 


45 


43 


42 


38 


40 


25 


34 


43 


52 


41 


23 


29 


22 


33 


27 


36 


40 


32 


40 


18 


32 


30 


43 


46 


20 


31 


19 


31 


42 


30 


40 


24 


41 


12 


30 


35 


33 


46 


33 


29 


24 


29 


35 


33 


41 


16 


23 


13 


28 


31 


34 


35 


17 


23 


12 


27 


32 


44 


29 


16 


23 


10 


26 


30 


23 


40 


13 


28 


7 


25 


34 


16 


39 


18 


32 


14 


24 


37 


23 


42 


9 


23 


3 


23 


38 


26 


27 


15 


13 


10 


22 


26 


19 


16 


3 


27 


5 


21 


30 


21 


30 


13 


14 


5 


20 


39 


10 


25 


11 


18 


4 


19 


23 


9 


21 


5 


24 


4 


18 


22 


6 


24 


7 


14 


1 


17 


21 


6 


16 


9 


18 


2 


16 


30 


9 


18 


9 


21 


1 


15 


24 


13 


22 


6 


20 




14 


26 


8 


17 


7 


10 


1 


13 


23 


8 


14 


5 


7 


2 


12 


21 


5 


18 


5 


10 




11 


22 


2 


15 


4 


8 


1 


10 


23 


8 


9 


2 


8 




9 


23 


6 


16 


4 


5 




8 


25 


1 


9 


2 


4 




7 


18 


2 


10 


3 


5 


1 


6 


12 


3 


7 


1 


2 




5 


10 




6 


3 


6 




4 


16 




12 




2 




3 


11 


4 


11 


2 


4 




2 


11 


4 


6 


2 


1 


1 


1 


12 


3 


10 


1 


1 







15 


3 


4 




1 




Total 


1342 


1539 


1427 


1338 


1136 


876 


Median 


28.6 


39.4 


32.8 


41.8 


35.1 


43.0 



52 ^ 

pupils of a grade exhibit a wide range of ability is a well known fact. We 
also know that there is a very large degree of over-lapping between successive 
grades. Probably all would admit that a grouping of pupils for purposes 
of instruction exhibiting such great differences in spelling ability does not make 
for the most effective instruction. Correction of this condition is sometimes 
difficult. In ungraded schools or in rooms where there are two or more grades, 
it is relatively easy to group the children for spelling instruction, but in rooms 
where all the pupils belong to the same grade this is more difficult. The 
pupils who make perfect scores or scores nearly perfect might be excused from 
spelling but this would not take care of those most needing instruction. 

In view of the fact that the time devoted to spelling is more frequently 
used in testing spelling than in teaching spelling, this table suggests that there 
is a definite need for teaching some pupils to spell. Some pupils appear to have 
learned to spell under the type of " instruction " which the schools now provide, 
but a large number of pupils have not done so. These pupils require a different 
type of "instruction." They probably need some assistance in learning to 
spell. 

Spelling errors. In the 1917 testing, several cities returned, in addition 
to the class record sheets on which were recorded the scores, the test papers. 
The specific errors in spelling the test words have been carefully tabulated for 
430 third grade pupils, 463 fourth grade pupils, 294 fifth grade pupils, 188 
ninth grade pupils, 120 tenth grade pupils, 107 eleventh grade pupils, and 169 
twelfth grade pupils. This study of errors was not extended as originally 
planned to the pupils in the sixth, seventh, and eighth grades because of a lack 
of funds. 

The fundamental reason for giving tests is to secure information concern- 
ing the abilities of pupils. In order that this information may be most helpful 
to us it is necessary that we interpret the scores in terms of pupil needs. The 
fact that a pupil has a certain score and that this score is above standard or 
below standard becomes significant to the teacher only when this fact is ex- 
pressed in terms of the learning needs of this pupil. In the case of scores 
below standards we have only partially interpreted them when we say that the 
pupils having such scores need to place more emphasis upon their spelling or 
that they need assistance from the teacher. We carry the interpretation a 
step further when we specify what words the pupils need to give their attention 
to. W^e may carry our interpretation another step by ascertaining the par- 
ticular errors which the pupils are making and hence need to correct. 

The tabulations of the misspellings show that some ways of misspelling 
a word occur much more frequently than others. In general about 60 percent 
of the misspellings belong to one of five kinds and about 30 percent are included 
in one. If a teacher knows the types of misspellings which are most likely to 



53 



TABLE XXIX. THE FREQUENCY OF MISSPELLINGS OF THE WORDS 
"COLLECT" AND "OMIT" AS FOUND IN THE TEST PAPERS 
463 FOURTH GRADE PUPILS. WHERE NO 
FREQUENCY IS GIVEN THE MIS- 
SPELLING OCCURRED ONLY ONCE. 
Collect Omit 



colect 


110 


culate 


omite 


35 


poment 


elect 


21 


cucket 


oment 


22 


phone 


deck 


9 


colest 


omet 


19 


omoit 


clet 


5 


connect 


omitt 


10 


amint 


celect 


4 


duck 


omeat 


10 


only me 


clack 


4 


polet 


ommit 


8 


eneat 


docket 


3 


coiker 


omitte 


6 


anete 


colcet 


3 


duct 


onit 


5 


enit 


cloct 


3 


coulack 


ownit 


5 


bremet 


cleat 


3 


cleick 


admit 


5 


obeat 


cluk 


3 


clach 


omnit 


3 


ument 


colet 


2 


clacket 


ament 


3 


opit 


col 


2 


klechit 


omnitt 


3 


omett 


collet 


2 


clich 


omt 


2 


oumient 


coloct 


2 


clank 


amit 


2 


omemt 


corlect 


2 


klocet 


ameit 


2 


portment 


cllect 





klucklect 


amite 


2 


owmet 


clock 


2 


clouct 


ornate 


2 


oneit 


culect 


2 


colict 


omeet 


2 


omant 


cocet 


2 


colcailate 


only 


2 


owe meat 


comelet 




clloe 


onipe 




connect 


ceaclect 




caluct 


omot 




obment 


calect 




clearty 


amite 




pomit 


somelet 




coloce 


omiet 




onitt 


golet 




colack 


poemet 




nent 


klited 




claxt 


omitted 




inate 


dontlet 




conckle 


onight 




oak 


kleke 




conut 


anitt 




onight 


kolicket 




coulet 


abment 




own 


cleakely 




coUice 


onet 






cault 




clecet 


comen 






celec 




colcect 


onent 






clecty 




cacated 


emmit 






codect 




cleclect 


amited 






colext 




clucker 


otamate 






collete 




clecket 


offit 






clllect 




cleack 


adnet 






collecks 




colucket 


aneat 






clete 




concect 


anint 






cole 




cart 


omoitte 






cleatlet 




lecke 


opote 






cherd 




coul 


ohmit 






colectt 




coleck 


omote 






cocllict 






obed 






kalat 






omip 






clectket 






amet 






cleakit 






tell me 






coluct 






anpend 







occur she can, in her teaching of spelling, warn pupils against the errors which 
they will most likely make and give them such training as may be required to 
insure that they will not make these errors. 

Because of the importance of giving attention to spelling errors, we give 
in Table XXIX the various misspellings of the words "collect" and "omit" 



54 

found in the examination of 463 fourth grade test papers. Some of the mis- 
spellings which Occur only once or at the most two or three times probably 
should not be counted as "true" misspellings. The writing of c-o-1 probably 
should be counted as an incomplete spelling. The writing of c-h-e-r-d indicates 
either that the pupil is not acquainted with the word "collect" or was unable 
to recall automatically the spelling, or failed to understand the word in the 
teacher's dictation. On the other hand the misspellings which recur frequently 
may be considered as "true" misspellings and are the ones which should be 
guarded against in the teaching of spelling. 

In interpreting spelling scores, we need to consider the questions, 
"Are all misspellings to be treated alike? Does one misspelling mean the same 



TABLE XXX. 



SHOWING MOST FREQUENT MISSPELLINGS OF THE TEST WORDS 
IN GRADE III BY 430 PUPILS 



Correct form 


No. of mis- 
spellings 




Five most frequent 


MISSPELLINGS 








OF 




















WORD 




1 


2 




3 




4 




5 




account 


218 


acount 


63 


count 


4f 


ocount 


10 


mony 


S 


accont 


5 


again 


177 


agin 


52 


agan 


40 


agen 


30 


agian 


14 


agun 


3 


almost 


157 


allmost 


101 


alnost 


18 


allnost 


12 


ailmast 


3 


amost 


2 


anyway 


105 


enyway 


27 


eneyway 


7 


inway 


5 


annyway 


4 


inyway 


4 


army 


115 


armey 


19 


amy 


15 


arme 


15 


armer 


5 


armay 


4 


begin 


169 


began 


4? 


begain 


36 


begun 


22 


begen 


16 


begine 


6 


begun 


196 


began 


49 


begin 


37 


begain 


30 


begone 


9 


begon 
besied 


9 


beside 


89 


by 


29 


besid 


20 


becide 


5 


besaid 


3 


2 


both ■ 


72 


those 


21 


bout 


6 


bothe 


3 


boath 


3 


bot 


3 


bought 


185 


bot 


85 


bout 


19 


brought 


13 


bough 


11 


boght 
chanse 


6 


change 


165 


chang 


2S 


Changs 


14 


chain 


11 


chanes 


10 


6 


children 


135 


childern 


25 


childen 


12 


chirdlren 


5 


childred 


5 


childer 


3 


collect 


219 


colect 


36 


elect 


26 


clact 


4 


clet 


4 


clack 


3 


contract 


172 


contrack 


49 


contrach 


5 


contrect 


4 


contrackec 


4 


contrak 


4 


deal 


167 


deel 


45 


dill 


28 


dell 


27 


dile 


17 


del 


6 


died 


120 


dide 


50 


did 


IP 


dided 


13 


dead 


7 


diead 


2 


dress 


55 


drees 


12 


dreess 


8 


drass 


8 


dres 


2 


dreass 


2 


drill 


69 


dril 


21 


drell 


7 


dill 


5 


grill 


4 


drail 


3 


driven 


77 


drive 


11 


driving 


5 


dreven 


5 


drivin 


5 


drivan 


4 


enter 


159 


inter 


71 


anter 


13 


enture 


7 


intre 


4 


ender 


4 


extra 


174 


extry 


3£ 


exter 


10 


antra 


5 


extery 


4 


extray 
do 


4 


few 


134 


you 


48 


fue 


32 


to 


8 


flew 


6 


4 


follow 


123 


folow 


14 


foller 


8 


fallow 


7 


folio 


6 


flow 


6 


goes 


162 


gose 


4C- 


gos 


47 


go 


44 


goese 


2 


goe 
grad 


2 


great 


18S 


grate 


91 


grat 


33 


graet 


10 


grait 


8 


3 


income 


140 


incom 


12 


incone 


8 


come 


5 


encome 


2 


incume 


1 


inform 


107 


inforn 


17 


reform 


12 


infrom 


9 


imform 


6 


informe 


6 


members 


122 


menbers 


IS 


meners 


9 


mambers 


8 


mebers 


5 


mimbers 


4 


might 


155 


mite 


78 


mit 


24 


mint 


11 


night 


5 


mighe 


3 


money 


126 


mony 


63 


many 


9 


maney 


8 


noney 


3 


momy 


3 


month 


149 


mounth 


42 


moth 


30 


mouth 


17 


mount 


9 


mont 


7 


office 


138 


ofice 


23 


offic 


21 


offes 


16 


offer 


8 


ofis 


7 


omit 


188 


omet 


25 


omite 


21 


oment 


15 


onit 


14 


omeat 


11 


paid 


167 


pade 


51 


payed 


32 


pad 


28 


pay 


18 


payd 


5 


past 


119 


passed 


30 


pass 


22 


pas 


9 


pasted 


7 


pask 


4 


picture 


131 


pitcher 


17 


picher 


13 


pictur 


9 


pictors 


7 


pctcure 


7 


please 


165 


pleas 


77 


plese 


17 


pies 


8 


pleace 


7 


place 
prove 


6 


provide 


128 


provied 


10 


provid 


8 


proved 


8 


proveid 


7 


5 


railroad 


111 


railrode 


12 


rayroad 


7 


ralroad 


4 


railroat 


3 


roilroad 


3 


ready 


144 


redy 


36 


rady 


22 


read 


9 


redey 


7 


rade 


5 

3 


recover 


120 


cover 


22 


uncover 


20 


recove 


f 


recuver 


8 


recome 


return 


98 


reture 


1.3 


returne 


7 


retun 


5 


returne 


4 


retern 


4 


says 


138 


sais 


IS- 


said 


17 


say 


13 


saids 


10 


sas 


9 


those 


140 


thoes 


76 


thos 


14 


thouse 


6 


thous 


5 


thoses 


4 


ticket 


69 


tick 


If 


ticked 


5 


tickit 


3 


ticke 


3 


tecket 


3 


took 


88 


tuck 


16 


tock 


13 


take 


7 


tooke 


5 


tuk 


5 


unable 


82 


unabel 


10 


onabel 


6 


unabil 


5 


unble 


5 


onable 


5 


understand 


83 


unstand 


13 


under 


5 


understant 


5 


undestand 


4 


understend 


3 


while 


109 


whil 


22 


wile 


21 


whill 


11 


will 


10 


why 


6 


who 


124 


how 


48 


ho 


35 


hoe 


8 


hew 


6 


hoo 


2 


Total 


6743 


1845 


903 


544 


331 


221 


Percent 




27 


13 


8 


5 


3 



ss 

as any other misspelling?" Does "colect" have the same meaning with refer- 
ence to the pupil's need for instruction as "connect" or "cole" or "ceaclect?" 
Probably all misspellings do not indicate the same instructional needs. The 
•writing of "colect," as was done by nearly one-fourth of all these fourth 
grade pupils, indicates uncertainty concerning the double consonant or a 
wrong habit formed. "Connect" probably indicates that the word was 
misunderstood. "Ceaclect" indicates the lack of a fixed habit and possibly 
that the pupil was not acquainted with the word. 

In Tables XXX, XXXI, and XXXII, we give a list of the five most 
frequent misspellings^^ of the test words in grades III, IV and V. The column 

TABLE XXXI. THE MOST FREQUENT MISSPELLINGS OF THE TEST WORDS IN 
GRADE IV BY 463 PUPILS 



COBRBCT FORM 


No. of mis- 
spellings 


FiVEMOST FREQUENT MISSPELLINGS 


OF 






















WORD 




1 




2 




3 




4 




5 




account 


246 


acount 


104 


count 


42 


ocount 


12 


accont 


7 


acont 


7 


again ', 


101 


agin 


40 


agan 


27 


agian 


jp 


agen 


i. 


agine 


2 


almost 


136 


aiimost 


83 


alnost 


2t 


most 


3 


alnose 


2 


almos 


1 


anyway 


76 


enyway 


21 


eneyway 


7 


any 


6 


inyway 


5 


anway 


2 


army 


78 


armey 


17 


amy 


9 


arm 


7 


arme 


4 


arney 


4 


begin 


137 


began 


52 


begain 


33 


begen 


If 


begun 


r. 


begon 


2 


begun 


200 


began 


5C 


begin 


33 


begain 


2i 


begon 


IC 


becine 


8 


beside 


55 


besid 


21 


by 


S 


becide 


5 


besde 


2 


aside 


2 


both 


77 


bouth 


16 


those 


14 


bough 


10 


bo the 


6 


bought 


5 


change 


144 


chang 


21 


changes 


11 


changed 


S' 


chanes 


S 


chane 


8 


children 


63 


chirldren 


11 


childern 


6 


chirlden 


5 


chrildren 


4 


chidern 


3 


collect 


257 


colect 


110 


elect 


21 


deck 


b 


clet 


5 


celect 


4 


contract 


178 


contrack 


4S 


comtract 


25 


contrat 


8 


concrat 


7 


contrach 


6 


deal 


106 


deel 


26 


dell 


24 


del 


6 


dill 


6 


dile 


4 


died 


72 


dide 


2r 


die 


S 


dided 


6 


did 


6 


Died 


3 


dress 


31 


drees 


7 


dreess 


z 


dres 


3 


Dress 


2 


drese 


2 


drill 


59 


dril 


IC 


drell 


7 


dill 


4 


trill 


3 


Drill 


2 


driven 


66 


drivin 


< 


dreven 


4 


drive 


£ 


drivvin 


S 


driver 


3 


enter 


99 


inter 


61 


enten 


3 


entere 


c, 


anter 


3 


ender 


3 


extra 


159 


extry 


45 


extray 


i 


extery 


6 


exter 


5 


axtra 


4 


few 


132 


you 


56 


fue 


32 


fiew 


5 


tue 


3 


fhew 


2 


follow 


97 


fallow 


IE 


flow 


11 


folow 


10 


fUow 


6 


foller 


5 


goes 


88 


go 


34 


gose 


30 


gos 


17 


gois 


2 


was 


2 


great 


95 


grate 


62 


geart 


5 


grat 


4 


greate 


4 


gred 


3 


income 


90 


incone 


1? 


incom 


16 


encome 


7 


incon 


4 


icome 


3 


inform 


132 


inforn 


33 


imform 


16 


informe 


13 


enform 


7 


enforn 


6 


members 


129 


menbers 


31 


membors 


7 


memers 


6 


meners 


5 


membes 


3 


might 


121 


mite 


57 


mit 


14 


mint 


14 


migh 


5 


night 


4 


money 


79 


mony 


4f 


noney 


7 


nony 


2 


momey 


2 


moeny 


2 


month 


114 


mounth 


31 


mouth 


18 


nounth 


11 


moth 


6 


mount 


5 


office 


94 


ofice 


20 


ofic 


15 


ofRc 


6 


offer 


6 


offece 


5 


omit 


205 


omite 


3.- 


oment 


22 


omet 


19 


omitt 


10 


omeat 


10 


paid 


103 


payed 


5C 


pade 


15 


pad 


12 


paied 


6 


Paid 


2 


past 


69 


passed 


21 


pass 


18 


pas 


5 


pasted 


4 


pass 


2 


picture 


75 


pitcher 


U 


pitcure 


10 


Picture 


2 


pictur 


3 


pictor 


3 


please 


121 


pleas 


66 


plese 


14 


plase 


5 


plise 


5 


pleace 


4 


provide 


160 


provied 


ID 


provid 


12 


pervide 


8 


proved 


5 


porvide 


4 


railroad 


73 


railrode 


21 


ralrode 


3 


railrad 


3 


roilroad 


2 


Rail Road 


2 


ready 


78 


redy 


27 


rady 


ir 


reddy 


6 


read 


3 


raid 


2 


recover 


118 


cover 


40 


uncover 


17 


recove 


12 


recuver 


6 


rncover 


3 


return 


62 


returne 


11 


retun 


8 


retern 


8 


retrun 


4 


retune 


3 


says 


105 


said 


24 


sais 


16 


say 


4 


ses 


6 


saids 


6 


those 


96 


thoes 


5)- 


thos 


10 


thouse 


4 


thoese 


3 


t hoses 


3 


ticket 


46 


tick 




tichet 


5 


ticet 


3 


tictect 


2 


tickt 


2 


took 


47 


tuck 


IC 


tock 


^ 


toke 


7 


tuke 


2 


take 


2 


unable 


73 


anable 


le 


enable 


e 


unabel 


5 


inable 


5 


uable 


5 


understand 


61 


unstand 


IS 


understad 


5 


undersand 


4 


understan 


3 


undestand 


3 


while 


61 


whil 


16 


will 


8 


whill 


7 


wile 


5 


whal 


5 


who 


69 


how 


2(i 


ho 


22 


Hew 


5 


wow 


3 


whow 


2 


Total 


5133 


1683 


7 


14 


383 


236 


173 


Per Cent 




33 


u 


7 


5 


3 



56 

headed "number of misspellings" gives the total number of misspellings. 
In the following columns the five most frequent misspellings are given with 
their frequencies. 

The column giving the total number of misspellings shows clearly that 
these words were not equal in difficulty for these pupils, although they were 
taken from the same columns of Ayres ' Scale. This condition indicates a 
limitation of that scale. This may be due to the fact that in deriving the scale 
Ayres used scores from many different states and hence the evaluation of the 
words was more general. It may also be due to the use of the scale as a mini- 
mum essential list. A third reason may be the nature of the test which was 
used. 



TABLE XXXII. 



THE MOST FREQUENT MISSPELLINGS OF TEST WORDS IN GRADE V, 
BY 294 PUPILS 



Correct form 


No. OF 






Five most frequent misspellings 


OF 


misspellings 












WORD 






















1 




2 


3 




4 


5 


action 


35 


actin 


3 


acionn 


3 


axion 


1 


actshon 


1 


axchian 


1 


addition 


127 


addion 


24 


adition 


21 


addation 


8 


addtion 


8 


additon 


8 


attempt 


144 


atempt 


34 


attemp 


12 


attenpt 


11 


etempt 


6 


atemp 


6 


await 


13G 


awake 


62 


awate 


18 


awaked 


13 


wait 


8 


awaite 


4 


claim 


145 


clame 


79 


plain 


12 


clam 


12 


clain 


n 


claime 


6 


command 


111 


comand 


62 


comman 


5 


commend 


4 


commad 


4 


comend 


4 


connection 


95 


conection 


47 


conecton 


4 


coniction 


3 


conections 


2 


connect 


2 


declare 


152 


declared 


65 


declair 


17 


declaired 


7 


declar 


6 


deelard 


5 


due 


78 


dew 


35 


do 


2E 


doe 


3 


du 


2 


doo 


2 


effort 


122 


efTert 


28 


efert 


21 


efort 


15 


effer 


6 


effor 


5 


Either 


155 


Eather 


99 


Ether 


20 


Eathe 


3 


either 


2 


Eaither 


2 


employs 


178 


imploys 


43 


employes 


17 


inploys 


13 


imployes 


10 


employ 


7 


entire 


123 


intire 


80 


inter 


7 


intier 


6 


intiar 


3 


intre 


2 


estate 


99 


astate 


41 


state 


23 


asstate 


4 


estait 


2 


states 


2 


direction 


84 


dirrection 


14 


drection 


10 


way 


7 


derection 


5 


driction 


3 


famous 


109 


famious 


27 


famis 


10 


famos 


7 


fames 


5 


f am est 


5 


field 


33 


feild 


22 


fields 


2 


feeld 


1 


feilds 


1 


fieled 


1 


firm 


69 


ferm 


17 


firn 


11 


furm 


9 


fern 


8 


form 


3 


forward 


74 


foward 


28 


foreward 


14 


frward 


3 


fored 


1 


forwar 


1 


factory 


72 


factor 


13 


facture 


8 


factry 


4 


fatory 


3 


factiory 


3 


final 


88 


finel 


34 


finial 


11 


finally 


5 


fineal 


3 


finall 


3 


gentlemen 


113 


gentleman 


41 


Gentlemen 


9 


gentle 


5 


gentlmen 


4 


gentlenen 


3 


important 


117 


importent 


18 


inportant 


7 


inportent 


7 


importanc 


6 


imporant 


6 


information 


129 


imformation 


32 


infermation 7 


message 


5 


imfermationS 


infomation 


3 


measure 


55 


masure 


24 


mesure 


3 


maisure 


2 


meashure 


1 


maisure 


1 


present 


57 


presant 


13 


preasant 


3 


preasent 


3 


prisent 


2 


presint 


2 


president 


131 


President 


33 


presedent 


9 


Presdent 


6 


Presedent 


4 


presedient 


3 


Prompt 


123 


Promp 


40 


prompt 


13 


Promt 


7 


Promped 


6 


pronpt 


4 


property 


89 


propty 


24 


proptery 


9 


propity 


6 


propety 


5 


propery 


4 


progress 


101 


progus 


S 


progess 


8 


progres 


8 


prograss 


5 


progrees 


3 


position 


289 


possion 


42 


postion 


34 


posion 


25 


physician 


9 


possition 


7 


region 


137 


regin 


20 


regon 


20 


reigon 


12 


reagon 


12 


regen 


7 


Remember 


156 


Rember 


93 


rember 


12 


Remcber 


8 


Remmber 


6 


remember 


4 


represents 


132 


repesents 


16 


repersents 


13 


represent 


13 


repersent 


4 


reperzents 


3 


result 


30 


rezult 


4 


reselt 


3 


ruselt 


2 


resuled 


2 


it 


2 


Saturday 


123 


Saturday 


37 


Saterday 


27 


Sat. 


E 


Saturdy 


5 


Satuarday 


5 


section 


54 


sextion 


9 


secton 


6 


sexion 


2 


sexton 


2 


Section 


1 


statement 


97 


statment 


41 


stament 


5 


statemet 


4 


satment 


3 


statemen 


3 


special 


104 


speeil 


11 


specal 


11 


spechal 


3 


speshtl 


a 


speacle 


3 


Suppose 


188 


Supose 


67 


suppose 


56 


Sopose 


19 


Soppose 


o 


supose 


3 


surprise 


183 


suprise 1 


03 


supprise 


26 


suprize 


7 


surprize 


6 


supprize 


3 


Sometimes 


46 


Sometine 


13 


Sometines 


6 


Sometine 


5 


Sometime 


3 


Sontimes 


3 


whom 


96 


shome 


17 


hom 


14 


home 


13 


who 





hoom 


9 


Whose 


127 


Whos 


31 


Sho's 


23 


Who 


21 


Whoes 


16 


whos 


7 


women 


S3 


wemon 


24 


wemen 


13 


woman 


11 


weman 


10 


wimen 


4 


wonderful 


86 


wounderful 


23 


wonder 


8 


wondful 


8 


woundful 


15 


wonderfull 


5 


Total 


5075 


16 


42 
32 


619 


3 


46 

7 


239 


173 


Per Cent 




12 






5 


3 



'^This includes in certain cases, the wrong use of the capital letter. A test word be- 
ginning a sentence was counted wrong if not capitalized. A test word which should be 
begun with a capital letter v/as counted wrong if the pupil failed to do this. 



57 



APPENDIX 

In the following tables, 5, 10, 20 30, 40, 50, 60, 70, 80, 90 and 95 percentile scores are 
given for several tests. In general these are tests which have been widely used and which 
appear to have some permanence. The interpretation of a percentile score is similiar to 
that of a median. In fact the 50-percentile score is the median. The 20-percentile score is 
the score above which there are eighty percent of the scores and below which there are 
twenty per cent. These tables are to be used for determining the position which a pupil 
occupies in the total distribution of his grade. 

TABLE I. MONROE'S STANDARDIZED REASONING TESTS IN ARITHMETIC 
FORM I. PERCENTILE SCORES BASED ON APRIL TESTING 

Correct Answer 









Grade 




Percentile 
























IV 


V 


VI 


VII 


VIII 


95 


16.5 


21.1 


20.0 


23.5 


18.4 


90 


14.4 


19.1 


17.8 


21.2 


16.5 


80 


11.7 


16.5 


14.9 


18.5 


14.0 


70 


9.9 


14.7 


13.2 


16.5 


12.1 


60 


8.4 


13.0 


11.7 


14.9 


10.4 


50 


7.0 


11,3 


10.4 


13.4 


9.0 


40 


5.9 


9.7 


9.0 


11.9 


7.5 


30 


4.7 


8.0 


7.6 


10.4 


5.9 


20 


3.5 


6.2 


6.0 


8.5 


4.2 


10 


2.0 


4.0 


4.0 


6.0 


2.4 


5 


1.1 


2.4 


2.8 


4.0 


1.4 


No. of 












pupils 


2968 


2996 


3518 


2803 


2515 



Correct Principle 



95 


26.7 


33.8 


26.5 


28.9 


29.6 


90 


23.0 


31.5 


23.8 


27.9 


26.6 


80 


18.5 


27.5 


20.7 


25.5 


24.0 


70 


15.6 


25.7 


18.2 


23.2 


21.8 


60 


13.3 


22 2 


16.0 


21.4 


19.5 


50 


11.3 


19.2 


14.2 


19.7 


17.2 


40 


9.2 


16.4 


12.7 


17.7 


15.1 


30 


7.2 


13.7 


11.1 


15.4 


12.7 


20 


5.2 


10.3 


9.2 


13.0 


9.9 


10 


2.8 


6.4 


6.6 


9.9 


6.4 


5 


1.1 


3.9 


4.7 


7.5 


4.1 


No. of 












pupils 


2932 


3027 


3498 


2706 


2472 



Rate 





.Oi^.-X-S' 










95 


16.4 


23.4 


18.1 


20.4 


17.3 


90 


14.5 


19.5 


15.5 


18.3 


14.9 


80 


11.8 


15.9 


12.9 


15.4 


12.0 


70 


10.0 


14.0 


11.4 


13.7 


10.1 


60 


8.7 


12.3 


10.0 


12.3 


8.6 


50 


7.8 


11.2 


8.7 


11.2 


7.5 


40 


6.7 


9.9 


7.9 


9.9 


6.6 


30 


5.7 


8.6 


7.0 


8.6 


5.7 


20 


4.5 


7.4 


5.8 


7.6 


4.7 


10 


3.0 


5.4 


4.2 


6.1 


3.2 


5 


1.7 


3.8 


3.0 


5.1 


1.8 


No. of k 












pupils ^ 


1412 


1705 


1699 


1717 


1642 



58 



TABLE II-A. MONROE'S STANDARDIZED SILENT READING TEST. COMPRE- 
HENSION. PERCENTILE SCORES BASED OM MAY TESTING. 

Form 1 





Percentile 


Grade 




III 


IV 


V 


VI 


VII 


VIII 


fix 


X 


VI 


XII 




95 


20.8 


24.2 


33.8 


38.6 


39.4 


43.9 


51.5 


50.1 


51.8 


58.4 




90 


14.4 


20.0 


26.7 


34.0 


35.7 


40.4 


43.3 


45.0 


42.1 


51.7 




80 


11.2 


16.5 


22.6 


28.3 


30.1 


35.4 


36.3 


39.0 


40.0 


42.5 




70 


8.9 


14.0 


19.4 


24.2 


26.5 


31.6 


31.0 


33.9 


35.9 


40.2 




60 


7.0 


12.2 


17.1 


20.2 


23.6 


27.5 


27.3 


29.8 


32.1 


36.5 




50 


5.2 


10.5 


14.9 


18.8 


21.0 


24.1 


24.0 


25.8 


28.5 


33.3 




40 


4.1 


8.7 


13.2 


16.7 


18.8 


23.6 


20.8 


21.4 


26.0 


30.5 




30 


3.1 


7.0 


11.4 


14.5 


16.8 


19.4 


17.6 


19.0 


23.2 


25.1 




20 


2.0 


5.1 


9.4 


12.0 


14.6 


16.7 


14.3 


16.1 


20.2 


21.7 




10 


1.0 


2.6 


6.2 


9.0 


11.4 


13.1 


10.7 


10.3 


15.3 


16.1 




5 


.5 


1.3 


4.0 


6.1 


9.4 


10.8 


7.4 


8.2 


11.6 


11.3 


N 


Limber of pupils 


1464 


1805 


1729 


1871 


1270 


1337 


783 


397 


236 


230 













Form 2 














Percentile 


Grade 




























III 


IV 


V 


VI 


VII 


VIII 


IX 


X 


XI 


XII 




95 


21.0 


27.2 


29.7 


39.6 


43.8 


45.8 


48.6 


52.4 


56.3 


58.9 




90 


17.6 


24.1 


27.2 


36.0 


40.0 


42.9 


41.7 


46.1 


49.7 


51.8 




80 


13.6 


20.3 


24.6 


31.1 


35.4 


38.5 


34.9 


39.1 


42.9 


43.6 




70 


11.0 


17.5 


22.3 


28.1 


32.2 


35.2 


30.8 


34.0 


38.0 


39.7 




60 


9.2 


14.9 


20.0 


25.6 


29.3 


32.6 


27.5 


30.1 


33.1 


35:9 




50 


7.9 


13.4 


17.9 


22.7 


27.0 


29.9 


24.5 


26.7 


29.4 


32.1 




40 


6.4 


12.0 


15.7 


19.7 


24.6 


27.6 


21.5 


23.5 


25.9 


28.4 




30 


5.0 


10.5 


13.5 


16.9 


21.4 


25.3 


18.2 


20.6 


22.8 


24.9 




20 


3.3 


8.5 


11.6 


14.0 


17.9 


21.6 


14.6 


16.7 


19.9 


20.3 




10 


1.7 


6.0 


8.0 


12.2 


14.1 


17.1 


10.2 


12.3 


15.1 


16.1 




5 


.8 


4.2 


6.5 


8.0 


11.3 


14.0 


6.8 


10.0 


11.3 


12.6 


N 


vmber of pupils 


8741 


10625 


10157 


9404 


8791 


7561 


781 


625 


443 


320 



Form 3 





Percentile 


Grade 




















III 


IV 


V 


VI 


VI 


VII 




95 


22.2 


25.1 


27.7 


41.9 


44.6 


46.0 




90 


19.4 


23.8 


25.6 


37.7 


41.7 


43.6 




80 


15.7 


21.3 


23.6 


31.9 


36.9 


39.9 




70 


13.4 


19.1 


22.2 


27.6 


32.9 


37.0 




60 


11.5 


17.1 


20.6 


24.8 


29.4 


35.3 




50 


9.6 


15.2 


19.0 


22.1 


26.5 


31.1 




40 


8.0 


13.5 


17.3 


19.4 


23.8 


28.3 




30 


6.4 


11.2 


15.3 


16.6 


20.4 


25.5 




20 


4.7 


9.0 


12.8 


13.8 


18.2 


22.1 




10 


2.3 


5.8 


10.1 


11.0 


13.7 


17.5 




5 


1.2 


3.3 


7.1 


8.5 


11.3 


13.9 


N 


amber of pupils 


1604 


1680 


1704 


1580 


1513 


1186 



59 



TABLE II-B. MONROE'S STANDARDIZED SILENT READING TEST. 
PERCENTILE SCORES BASED ON MAY TESTING 

Form 1 



RATE 



Percentile 



95 
90 
80 
70 
60 
50 
40 
30 
20 
10 
5 



Grade 



III 



98.0 
84.5 
70.7 
60.6 
52.2 
44.5 
38.0 
33.0 
20.6 
10.6 
5.2 



IV 



III.O 
105.9 
81.0 
80.6 
72.8 
65.2 
58.1 
51.7 
44.4 
34.3 
25.0 



Number of pupils 1464 1840 1828 1869 1279 1357 



143.5 
126.9 
110.0 
96.4 
87.0 
78.8 
73.0 
65.9 
56.7 
44.6 
34.6 



VI VII VIII IX 



145.4 

143.8 

115.5 

103.6 

95.3 

89.0 

73.0 

67.6 

60.2 

49.8 

41.1 



146.6 

142.7 

120.3 

110.9 

102.0 

95.1 

88.8 

82.8 

66.6 

58.2 

51.5 



148 

146 

142.7 

135.6 

115.1 

105.6 

97.2 

91.1 

82.5 

62.3 

53.4 



136.6 
120.9 
109.5 
100.8 



86, 
82, 
78. 
73. 
66. 
55. 



50.0 



785 



X 



143.0 
130 
120 
100 



84 

80.3 

75.6 

70.7 

61.5 

54.9 



397 



XI 



138.3 

130.9 

121.5 

105.0 

92.0 

86.6 

83.1 

79.5 

74.4 

67.9 

58.3 



235 



XII 



152.1 

137.4 

129.4 

122.7 

107.6 

102.7 

88.2 

84.2 

80.2 

69.2 

60.8 



220 



Form 2 



Percentile 



95 
90 
80 
70 
60 
50 
40 
30 
20 
10 
5 



Grade 



III IV 



117 
98 

78.0 
71.8 
67.0 
62.6 
55.7 
45.5 
36.8 
28.9 
15.5 



126.7 
122.2 
107.0 
96.9 
90.7 
76.6 
71.9 
67.1 
62.2 
49.5 
37.8 



128.4 

126.3 

122.1 

114.3 

104.6 

97.2 

91.5 

76.9 

71.3 

63.1 

55.4 



VI VII VIII IX 



165.9 

161.7 

147.0 

•136.3 

124.3 

114.1 

107.8 

100.8 

82.7 

72.1 

54.9 



167.2 
164.4 
157.3 
146.0 
137.4 
131.5 
115.8 
109,1 
101.2 
80.5 
72.2 



168.0 
165.9 
161.8 
154.6 
145.2 
137.4 
131.5 
115.5 
107.7 
88.1 
79.7 



137.9 

130.4 

123.6 

107.6 

101.5 

87.2 

82.9 

78.1 

72.0 

62.9 

56.1 



X 



138.7 

132.2 

123.6 

107.2 

103.2 

88.6 

83, 

79.0 

74.1 

67.1 

57.2 



XI XII 



140.4 

134.1 

125.8 

109.8 

104.1 

89.0 

84.3 

79.6 

73.1 

61.9 

54.7 



147 

139 

130 

123 

107 

102.3 
87.6 
83.1 
77.5 
69.6 
59.8 



Number of pupils 9739 10579 10150 9853 8767 7681 



781 



626 



443 



322 



Form 3 





Grade 










III 


IV 


V 


VI 


VII 


VIII 


95 


123.3 


127.0 


128.3 


146.7 


148.3 


148.8 


90 


109.9 


123.9 


126.7 


142.8 


146.2 


147.2 


80 


99.4 


114.7 


123.3 


124.1 


141.9 


143.9 


70 


89.0 


106.6 


119.9 


114. Q 


124.6 


140.5 


60 


84.5 


101.6 


109.6 


107.7 


115.9 


124.0 


50 


80.0 


93.8 


105.6 


101.1 


109.0 


117.3 


40 


72.3 


86.9 


101.6 


94.1 


102.5 


112.2 


30 


55.1 


81.4 


94.2 


86.9 


95.0 


106.0 


20 


46.7 


72.6 


85.7 


79.6 


86.8 


98.3 


10 


42.7 


48.9 


75.6 


69.1 


77.5 


85.2 


5 


22.7 


43.8 


59.6 


59.2 


65.3 


76.5 


Numbc" of pupils 


1608 


1695 


1702 


1579 


1528 


1179 



60 



TABLE III-A. CHARTERS' DIAGNOSTIC LANGUAGE TESTS FOR GRADES 

III TO VIII. PRONOUNS. FORM I. PERCENTILE SCORES 

BASED ON MARCH TESTING. 



Percentile 


Grade 
















III 


IV 


V 


VI 


VII 


VIII 


95 


27.9 


27.7 


30.7 


32.2 


35.4 


38.9 


90 


24.8 


24.8 


27.5 


29.7 


33.3 


37.5 


80 


21.3 


21.5 


23.6 


26.9 


30.6 


35.0 


70 


18.5 


19.3 


21.7 


24.7 


28.4 


32.9 


60 


15.8 


16.9 


20.1 


22.9 


26.3 


31.1 


50 


13.6 


15.1 


18.5 


21.4 


24.5 


29.0 


40 


11.7 


13.5 


16.8 


19.7 


22.5 


26.9 


30 


9.9 


11.9 


15.2 


17.9 


20.7 


24.4 


20 


7.8 


10.0 


13.3 


16.0 


18.5 


21.3 


10 


5.1 


7.6 


10.9 


13.2 


15.5 


16.0 


5 


3.3 


5.8 


9.5 


10.6 


13.1 


10.9 


No. of pupils 


787 


864 


895 


1344 


1566 


1253 



TABLE III-B. CHARTERS' DIAGNOSTIC LANGUAGE TEST FOR GRADES 
III TO VIII. VERBS (FORMERLY VERBS A.) FORM I. PER- 
CENTILE SCORES BASED ON MARCH TESTING. 



Percentile 


Grade 
















III 


IV 


V 


VI 


VII 


VIII 


95 


29.2 


32.0 


34.4 


37.0 


36.3 


39.4 


90 


25.3 


29.0 


32.2 


34.3 


34.7 


38.4 


80 


20.5 


24.3 


29.5 


31.0 


32.7 


36.8 


70 


17.8 


21.6 


27.4 


28.1 


31.1 


35.5 


60 


15.0 


19.5 


25.4 


26.1 


29.4 


34.2 


50 


12.6 


17.7 


22.6 


24.3 


27.7 


32.8 


40 


10.8 


15.9 


20.7 


22.4 


25.6 


31.2 


30 


8.2 


13.9 


18.6 


20.2 


23.4 


29.6 


20 


6.2 


11.7 


15.3 


17.7 


21.5 


27.2 


10 


3.9 


8.8 


11.5 


13.6 


18.6 


23.4 


5 


2.7 


6.4 


7.4 


11.3 


16.4 


20.8 


No. of pupils 


365 


403 


373 


478 


539 


638 



61 



TABLE III-C. CHARTERS' DIAGNOSTIC LANGUAGE TEST FOR GRADES 

III TO VIII. MISCELLANEOUS A (FORMERLY MISCELLANEOUS) 

FORM I. PERCENTILE SCORES BASED ON MARCH TESTING 









Grade 






Percentile 




























III 


IV 


V 


VI 


VII 


VIII 


95 


27.9 


23.8 


22.3 


29.7 


31.9 


34.6 


90 


24.1 


18.6 


19.1 


26.6 


28.9 


31.6 


80 


15.9 


15.1 


16.9 


23.0 


25.8 


28.3 


70 


11.5 


12.6 


15.0 


20.6 


21.9 


26.2 


60 


8.7 


10.8 


13.3 


18.6 


19.7 


24.1 


50 


6.7 


9.3 


11.6 


16.5 


18.9 


22.3 


40 


5.7 


7.9 


10.2 


14.6 


17.2 


20.3 


30 


4.6 


6.4 


9.0 


12.7 


15.5 


17.9 


20 


3.3 


5.1 


7.3 


10.8 


13.4 


15.4 


10 


2.0 


3.4 


5.5 


8.5 


10.4 


12.0 


5 


1.4 


2.6 


4.1 


6.5 


7.9 


9.1 


No. of pupils 


386 


669 


668 


845 


758 


494 



TABLE III-D. CHARTERS' DIAGNOSTIC LANGUAGE TEST FOR GRADES 

III TO VIII. MISCELLANEOUS B (FORMERLY VERBS B). FORM I. 

PERCENTILE SCORES BASED ON MARCH TESTING 



Percentile 


Grade 
















III 


IV 


V 


VI 


VII . 


VIII 


95 


27.5 


31.7 


33.7 


38.7 


39.0 


38.5 


90 


20.2 


29.5 


31.5 


36.4 


37.2 


37.3 


80 


16.7 


25.9 


28.8 


33.5 


34.6 


35.7 


70 


13.3 


22.9 


26.4 


31.4 


32.8 


34.6 


60 


10.3 


20.2 


24.0 


29.4 


31.2 


33.4 


50 


7.9 


17.8 


22.0 


27.3 


29.4 


32.0 


40 


5.0 


14.6 


19.5 


24.7 


27.4 


30.7 


30 


3.7 


11.9 


16.9 


21.7 


25.4 


28.9 


20 


2.5 


9.4 


14.4 


18.0 


21.9 


26.7 


10 


1.3 


6.5 


10.9 


13.9 


18.2 


24.3 


5 


0.7 


3.7 


7.1 


10.2 


15.5 


21.2 


No. of pupils 


230 


430 


307 


475 


412 


294 



62 



TABLE IV. CHARTER'S DIAGNOSTIC LANGUAGE AND GRAMMAR TEST 

FOR GRADES VII AND VIII. FORM I. PERCENTILE SCORES BASED 

ON APRIL TESTING 





Pronouns 


Verbs 


Miscellaneous 


Percentile 


Grade 


Grade 


Grade 




VII 


VIII 


VII 


VIII 


VII 


VIII 


95 


27.9 


33.4 


36.4 


34.5 


20.9 


30.6 


90 


23.5 


32.5 


34.1 


31.5 


17.0 


26.4 


80 


17.6 


27.7 


27.4 


26.3 


12.9 


21.7 


70 


13.0 


24.0 


17.6 


21.3 


10.4 


17.0 


60 


10.2 


20.5 


11.8 


16.8 


7.8 


14.4 


50 


8.0 


17.1 


7.8 


14.0 


6.3 


11.9 


40 


6.3 


13.7 


5.0 


10.9 


5.1 


9.5 


30 


4.9 


10.2 


3.5 


8.3 


3.3 


7.2 


20 


3.5 


7.0 


2.3 


5.4 


2.3 


5.1 


10 


2.1 


4.2 


1.1 


3.0 


.9 


3.1 


5 


1.3 


3.0 


.5 


1.9 


.5 


2.2 


No. of pupils 


936 


657 


434 


497 


332 


362 



TABLE V-A. WILLING 'S SCALE FOR MEASURING WRITTEN COMPOSITION, 
STORY VALUE. PERCENTILE SCORES BASED ON MARCH TESTING 









Grade 






Percentile 




























IV 


V 


VI 


VII 


VIII 


IX 


95 


76.3 


89,9 


93.2 


95.7 


96.1 


95.3 


90 


66.1 


85.5 


88.2 


91.5 


96.0 


90.8 


80 


57.5 


77.7 


81.5 


88.1 


88.6 


87.5 


70 


52.1 


71.3 


76.8 


82.8 


84.6 


84.9 


60 


46.8 


65.0 


72.6 


78.0 


80.5 


82.2 


50 


41.5 


58.7 


68.1 


74.0 


76.6 


79.0 


40 


36.9 


52.8 


63.3 


69.2 


72.9 


73.8 


30 


32.7 


46.6 


58.0 


63.5 


68.7 


68.4 


20 


28.4 


40.2 


51.5 


50.1 


62.2 


62.3 


10 


24.2 


31.5 


43.1 


46.0 


54.7 


53.3 


5 


22.1 


26.0 


37.0 


37.4 


46.9 


43.6 


No. of pupils 


320 


579 


705 


692 


572 


129 



63 



TABLE V-B. WILLING 'S SCALE FOR MEASURING WRITTEN COMPOSITION, 

ERRORS PER 100 WORDS. PERCENTILE SCORES BASED 

ON MARCH TESTING 





Grade 


Percentile 
















IV 


V 


VI 


VII 


VIII 


IX 


95 


32.1 


28.8 


18.8 


18.1 


14.8 


11.9 


90 


31.7 


24.9 


16.0 


13.9 


11.9 


10.3 


80 


28.2 


19.4 


11.9 


10.8 


8.8 


7.9 


70 


23.9 


15.6 


9.9 


8.7 


7.4 


6.0 


60 


20.9 


12.5 


8.2 


7.3 


6.1 


5.2 


50 


18.5 


10.7 


6.8 


5.8 


5.2 


4.4 


40 


15.5 


9.3 


5.5 


4.8 


4.4 


3.6 


30 


13.0 


7.3 


4.2 


3.8 


3.6 


2.8 


20 


10.3 


5.3 


3.0 


2.6 


2.5 


1.9 


10 


7.3 


3.5 


1.6 


1.3 


1.2 


.9 


5 


5.4 


2.1 


.7 


.7 


..6 


.5 


No. of pupils 


327 


578 


702 


693 


473 


129 



TABLE VI. HARLAN'S TEST OF INFOR. 

MATION IN AMERICAN HISTORY 

PERCENTILE SCORES BASED 

ON MAY TESTING 



Percehtile 


Grade 








VII 


VIII 


95 


78.8 


95.2 


90 


70.9 


94.1 


80 


56.6 


92.2 


70 


54.0 


81.1 


60 


48.8 


74.9 


50 


43.9 


68.2 


40 


38.8 


56.7 


30 


31.9 


50.9 


20 


27.1 


41.3 


10 


20.1 


31.4 


5 


15.5 


27.7 


Number of pupils 


1109 


1691 



64 



TABLE VII. HOTZ'S FIRST YEAR ALGEBRA SCALES, SERIES A 
PERCENTILE SCORES BASED ON MAY TESTING 





Addition 


Multipli- 






Equations 






and 


cation and 


Problems 


and 


Graphs 




Subtraction 


Division 






Formulas 




Percentile 
















Grade 


Grade 


Grade 


Grade 


Grade 




IX 


X 


IX 


X 


IX 


X 


IX 


X 


IX 


X 


95 


11.7 


10.5 


10.4 


10.7 


10.6 


9.3 


12.3 


11.0 


8.0 


7.5 


90 


10.8 


9.7 


9.7 


10.0 


9.9 


7.6 


11.5 


10.4 


7.5 


6.9 


80 


9.6 


8.9 


8.7 


9.0 


9.0 


6.6 


10.3 


9.5 


7.2 


6.3 


70 


8.6 


8.4 


8.1 


8.4 


8.1 


5.9 


9.3 


8.8 


6.8 


5.8 


60 


7.7 


8.0 


7.6 


7.8 


7.3 


5.3 


8.6 


8.2 


6.5 


5.4 


50 


6.9 


7.3 


7.2 


7.4 


6.4 


5.0 


7.7 


7.9 


6.2 


5.0 


40 


6.3 


6.7 


6.6 


6.9 


5.7 


4.6 


7.0 


7.5 


5.8 


4.7 


30 


5.7 


6.1 


6.0 


6.2 


4.8 


4.1 


6.4 


7.0 


5.4 


4.3 


20 


4.8 


5.5 


5.4 


5.6 


3.8 


3.6 


5.7 


6.4 


5.0 


3.9 


10 


3.7 


4.3 


4.6 


4.9 


2.6 


2.9 


4.5 


5.5 


4.2 


3.3 


5 


2.9 


3.2 


4.0 


4.2 


1.5 


2.2 


3.7 


4.3 


3.7 


2.8 


Number of pupils 


561 


390 


570 


388 


566 


394 


478 


385 


121 


413 



TABLE VIII. HOLLEY'S SENTENCE VOCABULARY SCALES. PERCENTILE 
SCORES BASED ON APRIL TESTING 



Percentile 


Grade 


























II 


III 


IV 


V 


VI 


VII 


VIII 


IX 


X 


XI 


XII 


95 


72.7 


53.5 


45.2 


50.9 


65.5 


63.9 


66.5 


68.5 


75.2 


77.9 


82.3 


90 


68.5 


44.7 


40.0 


47.6 


61.0 


58.5 


62.6 


64.6 


70.0 


75.0 


78.2 


80 


63.8 


32.3 


35.7 


42.4 


54.7 


52.5 


57.4 


58.7 


66.0 


69.6 


73.1 


70 


59.6 


25.7 


31.6 


38.5 


49.2 


48.2 


54.2 


55.5 


61.8 


66.4 


68.8 


60 


57.2 


20.0 


28.2 


35.8 


46.2 


45.1 


50.9 


52.3 


58.7 


63.1 


65.8 


50 


54.8 


16.7 


25.1 


33.0 


42.8 


41.9 


47.8 


49.0 


56.1 


59.9 


62.8 


40 


52.4 


13.4 


22.1 


30.3 


39.5 


38.4 


44.7 


45.8 


53.4 


56.9 


59.7 


30 


50.0 


10.1 


18.7 


27.0 


35.5 


34.3 


41.6 


42.6 


50.8 


53.9 


56.3 


20 


46.1 


6.8 


14.7 


23.6 


31.4 


30.2 


36.8 


38.9 


46.6 


51.0 


52.8 


10 


42.2 


3.4 


10.7 


20.2 


24.9 


20.9 


30.0 


33.9 


41.6 


45.4 


48.3 


5 


40.3 


1.7 


6.0 


13.1 


21.1 


13.4 


22.8 


31.3 


37.4 


42.1 


44.1 


No. of 
























pupils 


117 


406 


520 


465 


450 


1188 


1047 


253 


223 


155 


108 



LIBRARY OF CONGRESS 

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